Home | Math | 10 Examples of Combinations in Math

10 Examples of Combinations in Math

September 14, 2023
written by Rida Mirza

Combinations are a fundamental concept in mathematics, and they arise in numerous everyday situations.

A combination is a selection of items from a larger set, where the order of selection does not matter.

In this article, we will discuss into 10 examples of combinations in math.

image showing the examples of combination

Examples of Combinations

Here are 10 examples of combination in math.

1: Selecting a Committee

Imagine you need to form a committee of five members from a group of ten qualified individuals. How many different combinations of committees can you create? To calculate this, we use the combination formula:


In this case, n represents the total number of individuals (10), and k represents the number of members you want in the committee (5). Plugging in the values:


So, there are 252 different combinations of forming a committee.

2: Lock Combinations

Lock combinations are an everyday example of combinations in action. Think of a standard padlock with three dials, each ranging from 0 to 9. How many possible combinations exist for this lock? The answer is 10^3=1,000.

3: Choosing a Pizza Topping

Let’s say you’re ordering a pizza, and the menu offers ten different toppings. You want to choose three toppings for your pizza. How many unique combinations of pizza toppings can you create? Again, we use the combination formula:


You have 120 different ways to top your pizza.

4: Passwords and Security

In the digital age, password security is crucial. Combinations are at the heart of creating secure passwords.

A common recommendation is to use a mix of uppercase letters, lowercase letters, numbers, and special characters.

5: Lottery Numbers

Lotteries involve combinations as well. Consider a lottery where you must choose six numbers from a pool of 49. The number of combinations is:


That’s almost 14 million different combinations for winning the jackpot.

6: Combinations in Genetics

In genetics, combinations come into play when considering the possible combinations of genes from parents to offspring.

Each child inherits half their genetic material from their mother and half from their father. This intricate mix of genetic combinations leads to the diversity of traits we see in living organisms.

7: Handshakes at a Party

Imagine you are at a party with ten people, and everyone shakes hands with everyone else once. How many handshakes occur at the party?

This scenario involves counting combinations, and the answer is C(10,2)=45 handshakes.

8: Combinations in Poker

Poker relies on combinations to determine the strength of a hand. Whether it’s a pair, a flush, or a full house, poker hands are evaluated based on the combinations of cards they contain.

9: Music Playlist

Creating a music playlist is another everyday example. If you have a library of 50 songs and want to make a playlist of 10 songs, there are C(50,10) possible playlist combinations.

10: Ice Cream Flavors

Lastly, consider a visit to an ice cream parlor with 15 different flavors. If you want to sample 5 different flavors, how many unique combinations can you create? Once again, the combination formula comes to the rescue:


You have 3,003 delightful ice cream flavor combinations to explore.

File Under: