Would you believe it if we said that while playing the piano or making a cup of coffee, you’re unknowingly applying mathematical concepts of permutation and combination? Most definitely not. But the truth is, you are!
There are several real-life situations where we use the knowledge we have learned in school about permutation and combination. But what exactly are they? While both terms are used together, they are not the same.
Permutation involves arranging a set of objects or data in sequential order and determining the number of ways it can be arranged. An important point to remember here is that the order of arrangement of objects/ data matters in permutation.
On the contrary, combination involves arranging or selecting objects/ data from a large set, and the arrangement or order of selection does not matter.
We have jotted down some interesting examples in this write-up to help you understand how these math concepts find their way into the real world. So, keep reading!
Real-life examples of permutations
1. Combination lock
A combination lock is a useful item that helps safeguard our belongings when we are out and about. Now, we all know that one can open a combination lock only when the perfect code, in the correct sequential order, is entered. If the code is not in the right order, it won’t open. To give you an example, if the lock code is 321, you will have to enter the code in the same sequence to open it. Entering 231 or 123 will not help.
2. Passwords
Every day we find ourselves typing passwords on our laptops or mobile phones. Passwords also help in keeping our digital information safe. Similar to a combination lock, passwords are also an arrangement of alphabets, digits, and characters in a particular order. These work only when we enter all the characters of the password in the correct sequence. A tiny misplacement here in there, and you cannot access your device.
3. Phone numbers
Phone numbers typically consist of different parts. For instance, in the phone number +1- 603-452-5521, +1 is the country code, 603 is the area code, 452 is the exchange code, and 5521 is the subscriber code. The first three sets of numbers are fixed depending on which area the phone number belongs. The last four numbers are permutations of digits to form a unique subscriber number. In its entirety, a complete phone number is also a permutation, as one must follow the same order to dial and connect to the right person.
4. Car plate numbers
Car license plates are another real-life example of permutation. The number of characters on a license plate varies across states as each state has its own way of numbering license plates. While some have 6-character plates with varying numbers of letters and digits, others have 7-character plates with similar variations. The department of motor vehicles issues license plate numbers to each car by applying different permutations to obtain unique numbers.
5. Playing the piano
When pianists play a song on the piano, they press a unique series of keys that produce specific notes that together form a musical piece. If the sequence of keys is not followed, they won’t be able to play the intended song. Therefore, the notes of a song are a permutation of piano keys, which, when played together in a predetermined sequence, produce beautiful music. Even a slight deviation in the sequence can cause a misplaced note that hampers the song’s melody.
6. Word formation
The English alphabet has only 26 letters. But the number of words we make out of these 26 letters is uncountable! This is possible because we use permutation to form smaller subsets of the large set of 26 letters. By arranging different letters in a set order, we have managed to create hundreds of words. Only when we write letters in the correct order, we make words that make sense.
Real-life examples of combinations
1. Making a cup of coffee
Make yourself a cup of coffee and observe the sequence in which you add milk, water, coffee, and sugar. Do you think your coffee will taste different if you add the ingredients in a different order to the cup? Not really. That’s because your coffee is a combination of its ingredients. It doesn’t really matter in which order you’re adding and mixing the ingredients to make a perfect cup of coffee for yourself.
2. Picking three finalists
Suppose there is a dance competition wherein the judges have to select three finalists for the last round out of seven participants. Here the concept of combination will come into play because the judges must pick three contestants in no particular order for the final round. All three will be a part of the finals and compete for the same winning position. Their order of performance in the finals will not affect their chances of winning the title.
3. Selecting 2 out of 5 questions
Another real-life example of combinations is when you have the option of solving a few questions out of a larger set of questions. Say, for example, your question paper mentions you can solve any two out of five questions in a section. That means you can solve multiple combinations like questions 1 and 2, 3 and 4, 4 and 5, 5 and 1, and so on. The order in which you solve the questions does not matter, but the answers do.
4. Selecting teams
Suppose for a school’s cultural event, a teacher wants to form a team, and she must select students from grades 9 and 10. She has a large set of students, out of which she must select a few to prepare a team for the event. There can be numerous combinations depending on the total number of students, but she can choose the team based on her judgment without worrying about the order in which she selects them.
5. Clothes combination
When you head out on vacation, you select only a few pieces of clothing to take along. If you carry three pairs of jeans and four t-shirts for your trip, you can combine them differently for various occasions to get a new look every single time. The order of pairing the clothes won’t matter, but the look of the outfit will. So, you can see how we unknowingly apply the concept of combination for a simple activity like clothes selection.
6. Ordering food
Admit it. Ordering food at a restaurant is never easy. There’s so much deliciousness on the menu which leaves us confused. So, what do we do? We select the best possible combination of foods to satiate our taste buds. While doing so, we pick items from the menu in random order and place our order. Our sequence of selection does not alter the taste of the food. The combination of dishes we select gives us a great dining experience.
In conclusion
When learning topics like permutation and combination, students often think they will never use them later in life. But that is not true. We use our knowledge in so many ways regularly. We just fail to appreciate why we’re able to do it. And that’s simply because we learned them in school. Real-life examples clarify our doubts and show how we use our learnings in daily life. We hope the examples shared in this write-up have enlightened you on how we practice our knowledge of permutation and combination to make our lives easier.
An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’,