How many ways can a committee of 3 be formed from 5 people?

How many ways can a committee of 3 be formed from 5 people?

Correct Answer: 10

Step 1: Understand that we need to form a committee of 3 people from a group of 5 people.
Step 2: Recognize that the order in which we choose the committee members does not matter. This means we will use combinations, not permutations.
Step 3: The formula for combinations is C(n, r) = n! / (r! * (n - r)!), where n is the total number of people, r is the number of people to choose, and '!' denotes factorial.
Step 4: In this case, n = 5 (the total number of people) and r = 3 (the number of people to choose).
Step 5: Plug the values into the formula: C(5, 3) = 5! / (3! * (5 - 3)!)
Step 6: Calculate the factorials: 5! = 120, 3! = 6, and (5 - 3)! = 2! = 2.
Step 7: Substitute the factorials back into the formula: C(5, 3) = 120 / (6 * 2).
Step 8: Calculate the denominator: 6 * 2 = 12.
Step 9: Now divide: 120 / 12 = 10.
Step 10: Therefore, there are 10 different ways to form a committee of 3 from 5 people.

Combinatorics – The study of counting, arrangements, and combinations of objects.
Binomial Coefficient – A way to calculate the number of ways to choose a subset of items from a larger set, denoted as C(n, k) or n choose k.