10 Engaging Games & Activities For Learning Permutation And Combination

The transition from learning elementary to higher mathematics calls for the sweat of one’s brow. This is the time when a student encounters concepts that he probably has never heard of before. One such topic is ‘Permutation and Combination.’

Permutations and Combinations are based on the fundamental principle of Counting. Both of these methods are used to find the number of possible outcomes in varied situations. Permutations refer to the idea of arranging different elements of a set in a predefined sequence, while a combination is more of a selection of some members of the set regardless of the order. 

Students can have a hard time understanding the differences between permutations and combinations if they fail to contemplate the logic behind them. In order to have a grip on the subject, it is important to enjoy the learning process. Therefore, in this post, we have compiled a list of online games and classroom activities to make sure that kids learn in a fun environment, and are ready to master the art of permutations and combinations!

Games and activities for introducing permutation and combination

1. Ice Cream by transum.org

Ice Cream by transum.org

The game uses the idea of ice creams to understand the concept of permutation and combination, which is a great way of learning math. The game is simple and easy to understand. Based on one question, how many different two-scoop ice creams can be made? Kids are given 6 different ice cream flavours using which they need to make as many differently-colored two-scoop ice creams can be made. 

The six flavours of ice cream in the game are lemon, strawberry, vanilla, peach, chocolate, and mint. The kid will have to tap on the flavour buttons to pour a scoop of ice cream into the cone below. Once you have filled two scoops of ice cream on a single cone, the cone is arranged on the rack above. This way, the user has to fill different cones with different flavours of ice cream to win the game.

2. Sudoku


The Sudoku game is a number-placement, logic-based game that represents a permutation problem for students to solve. It comes with a board that has a 9-by-9 square face – and is partially completed. The fundamental aim of the very game is to place the numbers 1 to 9 in each row, each column, and each of the 3-by-3 sub-boxes. While playing this game, you can ask the pupils questions like— How many different possible ways are there to play in the second column of numbers?; how many different possible ways are there to play in the second and third row of numbers?; How many different possible ways are there to play the entire game of Sudoku, including all nine rows? These questions will not only retain curiosity but also help promote learning.

3. Combination and Permutation Notation

 Combination and Permutation Notation

Much like the classroom quizzes, this is an online quiz that gives students plenty of permutation and combination problems to solve. These can be made easy or complex according to the level of the student. The online quiz game can be a great assessment tool for the students and can be used by teachers and parents. This P&C game is for learners who are beginning to learn the concept and even for students who have learned it and are on the verge of evaluation. This quiz would be fun even as a classroom activity, a homework activity, and even for homeschoolers. 

4. Striped Sweets

Striped Sweets

With 8 levels, this game is based on coloring the toffee wrappers in a way that all the wrappers look different from each other. Basically, two crayons, red and blue, are given in the game which a number of toffees with wrappers. In the first level, there are 4 toffees, in the second there are 8, and so on. The kids need to form such combinations using the concept of permutation and combination that each toffee wrapper looks different from the other. 

There are three boxes on each outer wrapper, which the kids need to color with the two colour options. The boxes are to be filled in such a way that each pattern is varied and different, and none of them are similar. Only when the player is able to create different patterns, they can cross the level. This game helps kids understand the concept of combination and helps them stimulate their brain so that forming combinations does not look like a heft task to them. 

5. Egg box investigation

Egg box investigation

In this game, two eggs have been given to the players to arrange in a crate of 6. But, the catch here is that the combination of putting the eggs should be different every time. On every turn, the player can click a snapshot of the combination that they have made with the eggs. Comparing the combinations, they need to make as many possible patterns so that each one looks different.

The game asks one question to the players – ‘In how many different ways can 2 eggs be arranged in a 6-pack egg box?’. The answer to this would be the many combinations that the player needs to make. The level does not get over until the number of patterns that can be made is exhausted. 

6. The Fruit Chunk Analysis:

An easy-peasy technique to help kids get their basics clear on permutations and Combinations is to introduce them to an activity we’d like to call ‘The Fruit Chunk Analysis.’ All you need is a cup of fruit chunks or colored grains for each group of students. Every group should count the number of each color fruit chunk and note down the data on a sheet. They should also count the total number of pieces. Thereafter, they can be asked to organise the different possible arrangements or to count the number of a specific selection. For example, you may instruct them to choose three different colors from the total number and ask how many ways they can make their choice. 

7. Choose the Hat:

For this activity, the parent or the educator needs to dig up the drama room and get some hats. Basically, the goal of the activity is to make a combination of 3 hats, which John (a fictional character) can wear throughout the week. Basically, in the activity, kids can assume that John has a habit of wearing hats, but he only has 3 hats which he has to wear by applying the permutation and combination strategy. 

The strategy needs to be such that each day he is able to wear a hat, and since there are 3 days and 5 weekdays, he would have to repeat hats on two days. Therefore, students can form multiple permutations and combinations with the hats to decide how many different ways there are in which John can wear his hats in one week.

8. Clothes to Outfits:

This activity requires students to make full-fledged outfits for the whole week. For this activity, the teacher or the parent needs to have cutouts of images of shirts, trousers, shoes, and accessories, which the students can combine and make into different outfits for all 6 days of the week. The aim is to make 6 different outfits from 3 shirts, 3 pairs of trousers, 2 pairs of shoes and 2 types of accessories. For example, if there are shirts which are pink, purple and black, and trousers which are black, white and beige along with black and brown shoes. The student can make the outfits as –

Monday- Pink shirt with black trousers and black shoes, and one accessory.

Tuesday- Purple shirt with brown trousers with brown shoes, and the other accessory.

Wednesday- Black shirt with beige trousers and black shoes with the first accessory.

Thursday- Pink shirt (again), but this time with brown trousers and brown shoes and the second accessory.

Friday- Purple shirt (again), but this time with beige trousers and brown shoes and the first accessory.

Saturday- Black shirt (again), but this time with brown trousers and no accessory. 

To amp it up a little, teachers can time the activity, which will make the students rush and be even more clear of the concept of permutations and combinations. 

9. What’s In The Menu?

This activity is based on a restaurant theme where the students need to curate the menu of a restaurant. But the catch here is that the restaurant caters the customers with only 4 types of vegetables with rice and noodle option, and the menu needs to have at least 8 food options. The challenge here would be to combine two vegetables together and serve them with either rice or noodles. The students can also combine three or more vegetables and make another dish, but there should be at least 8 items on the menu. This can be a great way to teach students combinations and the vitality of permutations.

For example, if the vegetables available are onions, carrots, mushroom, and baby corn, the students can curate the following dishes –

Combination 1- Noodles with fried onions.

Combination 2- Noodles with carrot and mushroom curry.

Combination 3- Noodles with baby corn and onion curry.  

Combination 4- Noodles with stir-fried carrot and baby corn. 

Combination 5- Rice with onion, carrots, and mushroom curry

Combination 6- Rice with fried mushrooms

Combination 7- Rice with stir-fried mushroom and baby corn.

Combination 8- Rice with onion and carrot soup. 

Moreover, there can be other ‘n’ number of combinations that the student can make. To level up this activity, educators can keep it time-based by asking students to make as many possible combinations in 10 minutes. The student who makes the most of them would win the game!

10. Lock-Unlock

To indulge in this activity, the teacher or the parents would need a lock, which has a combination lock in it. The idea of the game is to give students three random numbers and ask them to form as many combinations from the number as possible. One of the numbers would be the right number that opens the lock. For example- the lock opens with the number 982, so the teacher can give 2, 8, and 9 to the students. The students can make combinations like 289, 829, 928, 982, 298, and much more.

The student who unlocks the lock first by trying all the possible combinations wins the game. This activity can be made even more adventurous and interesting by placing not one but many locks. Like, the teacher can bring five locks, each with a different number code. The students would now have to make combinations out of 5 sets of numbers. Keeping this activity time-based can be great for students who wish to excel in this activity and concept. 

Need of permutation and combinations in our daily lives

While studying a lot of topics in Mathematics, students can wonder, ‘how am I going to use this practically?’ It can be algebra, LCM, or even the concept of permutations and combinations. However, this is one topic that, when mastered theoretically, can come into use practically too. 

These are the various events and occasions where the concept of permutations and combinations can be used avidly:

  1. Selection of Menu- For restauranteurs and even for individuals who love to cook their own meals— permutation and combinations come into use whenever they are deciding the menu for the day or are looking to try something new to cook. For example, you might think combining chicken with some broccoli might make up for a good meal. Or, you might just have a few ingredients lying around in your fridge, and you have to make a meal for yourself from those items only. In such a case, what would you do? You are left with brainstorming and combining the items which are left. 
  2. Selecting outfits- None of the outfits come pre-matched. You need to buy top wear and bottom wear separately and later combine them and make an outfit out of them. Not just with the outfit, this also goes for shoes, belts and much more. Forming a particular combination using P&C is essential for the everyday selection of clothes.
  3. Subjects- Students might have to time and again choose the various subjects they want to study. Here, the students have the data of no. of hours they have, the amount of syllabus to cover and the hard work they need in a particular subject.
  4. Phone Numbers- Including zero, there are a total of 10 digits in the number system. However, there are millions and billions of phone numbers that are being used around the world by the same 10 digits. The art of combining and permutating different numbers in a way to get a unique number every time also requires P&C. 
  5. Number Plates- A car’s number plate has a combination and a mix & match of a few numbers with letters. However, for every car, there is a unique number plate. To get a distinct one each time, there is a need for the concept of P&C all over the world. 

Apart from these daily-use activities, the concept of permutation and combinations are used in specific fields like –

  • Computer Architecture: In the arrangement of logic gates which is the bare necessity when it comes to computer architecture.
  • Computational Molecular Biology: P&C is avidly used in atoms, molecules, DNA, genes and much more when it comes to molecular biology.
  • Pattern Analysis: From visual images to pressure to temperature, the concept of permutation and combination is actively used in this branch to create patterns that are represented throughout the field. 
  • Database: Forming the sequence of digits, characters, bits and much more is all a part of database and data mining. For this purpose, P&C comes into use.

Best way to use these activities

Permutation and combination is a mathematical concept that is used in every phase of life. Therefore, the activities mentioned above would be super beneficial. But, how would you conduct these activities being a parent or an educator? Here are a few ways to do so!

  1. As classroom activities: While there is no denying that traditional teaching methods are nifty for kids of all ages, but activities too have their own set of vitalities. Therefore, indulging children in some activities during classroom studies can fetch educators really good results! These would make the learning process more fun and indulgent and would help students grasp better.
  2. During activity hours: Can you imagine your kid studying during activity hours? An activity period in the school is one time which every student looks forward to. But these activities when employed in the perfect setting, can result in a great blend of fun with learning. Therefore, executing these activities during play hours or activity time can be a great option while you teach the concept theoretically in the math class. 
  3. For evaluation purposes: Whenever we talk about ‘how to check the understanding of a particular concept,’ we think about just one thing, which is Examinations! But, on the contrary, these activities can be a substantially effective way to check whether or not the student has grasped the concept of permutation and combination. Moreover, the student would be more enthusiastic about the activity, and thus, it would be easy for the educator and parents to see whether or not the student has understood the concept.
  4. Holiday homework activity: Whenever the school is off for a long time, teachers tend to give out holiday homework so that the students do not lose touch with the concepts which were taught to them before the vacations. However, another challenge that they face of ‘which homework to include that the student is willing to do during vacations?’ And to answer this question, activities which involve the concept of P&C are perfect as these can be carried out easily at home, with friends, and during free time at home during vacations.
  5. For homeschooling: Parents and educators often find it arduous to keep homeschoolers engaged and find new and exciting ways to help homeschoolers learn better and in a fun way. And these activities would do just that. Parents and caretakers can help students indulge in these permutation and combination activities to grasp better and are eager to learn new things that they can relate to with real-life concepts. 

Concluding thoughts

An integral part of probability – a concept that is used in our everyday lives on a quotidian basis, permutations and combinations may seem tough or challenging at times. However, learning and understanding the concept of permutation and combination does not really have to be all about jotting down formulas or going about understanding it the conventional (often monotonous) way. 

Games are an innovative technology that piques the students’ interest in the subject and also makes the learning process comparatively more fun. On that note, we hope that our carefully curated list of online games and activities helps to teach and learn permutation and combination more engaging and fun.

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