How many ways can a committee of 3 be formed from 7 people? (2021)

How many ways can a committee of 3 be formed from 7 people? (2021)

Step 1: Understand that we need to choose 3 people from a group of 7 people.
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 = 7 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 7C3 using the formula: 7C3 = 7! / (3! * (7 - 3)!) = 7! / (3! * 4!).
Step 6: Calculate the factorials: 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1, 3! = 3 × 2 × 1, and 4! = 4 × 3 × 2 × 1.
Step 7: Simplify the expression: 7C3 = (7 × 6 × 5) / (3 × 2 × 1) = 210 / 6 = 35.
Step 8: Conclude that there are 35 different ways to form a committee of 3 from 7 people.

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.