If a committee of 4 members is to be formed from 8 people, how many different co
Practice Questions
Q1
If a committee of 4 members is to be formed from 8 people, how many different committees can be formed?
70
56
28
12
Questions & Step-by-Step Solutions
If a committee of 4 members is to be formed from 8 people, how many different committees can be formed?
Step 1: Understand that we need to choose 4 members from a group of 8 people.
Step 2: Recognize that the order in which we choose the members does not matter (i.e., choosing person A, B, C, D is the same as choosing D, C, B, A).
Step 3: Use the combination formula C(n, r) = n! / (r! * (n - r)!), where n is the total number of people (8) and r is the number of people to choose (4).
Step 4: Plug in the values into the formula: C(8, 4) = 8! / (4! * (8 - 4)!) = 8! / (4! * 4!).
Step 5: Calculate 8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1, but since we have 4! in the denominator, we can simplify: 8 × 7 × 6 × 5 / (4 × 3 × 2 × 1).
Step 6: Calculate the numerator: 8 × 7 = 56, then 56 × 6 = 336, and finally 336 × 5 = 1680.
Step 7: Calculate the denominator: 4 × 3 = 12, then 12 × 2 = 24, and finally 24 × 1 = 24.
Step 8: Divide the numerator by the denominator: 1680 / 24 = 70.
Step 9: Conclude that there are 70 different ways to form a committee of 4 members from 8 people.
