If a committee of 3 is to be formed from 5 people, how many different committees

If a committee of 3 is to be formed from 5 people, how many different committees can be formed?

If a committee of 3 is to be formed from 5 people, how many different committees can be formed?

Step 1: Understand that we need to choose 3 people from a group of 5.
Step 2: Recognize that the order in which we choose the people does not matter (i.e., choosing person A, B, and C is the same as choosing C, B, and A).
Step 3: Use the combination formula, which is written as nCr, where n is the total number of people and r is the number of people to choose. Here, n = 5 and r = 3.
Step 4: The combination formula is nCr = n! / (r! * (n - r)!), where '!' denotes factorial (the product of all positive integers up to that number).
Step 5: Calculate 5C3 using the formula: 5C3 = 5! / (3! * (5 - 3)!)
Step 6: Calculate the factorials: 5! = 5 × 4 × 3 × 2 × 1 = 120, 3! = 3 × 2 × 1 = 6, and 2! = 2 × 1 = 2.
Step 7: Substitute the factorials into the formula: 5C3 = 120 / (6 * 2).
Step 8: Calculate the denominator: 6 * 2 = 12.
Step 9: Now divide: 120 / 12 = 10.
Step 10: Conclude that there are 10 different committees that can be formed.

Combinatorics – The study of counting, arrangements, and combinations of objects.
Binomial Coefficient – The formula used to determine the number of ways to choose a subset of items from a larger set, denoted as nCr.