Question: From a group of 8 people, how many ways can a committee of 3 be formed?
Options:
56
24
8
12
Correct Answer: 56
Solution:
The number of ways to form a committee of 3 from 8 is C(8, 3) = 56.
From a group of 8 people, how many ways can a committee of 3 be formed?
Practice Questions
Q1
From a group of 8 people, how many ways can a committee of 3 be formed?
56
24
8
12
Questions & Step-by-Step Solutions
From a group of 8 people, how many ways can a committee of 3 be formed?
Correct Answer: 56
Step 1: Understand that we need to choose 3 people from a group of 8.
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 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 (3).
Step 4: Plug in the values into the formula: C(8, 3) = 8! / (3! * (8 - 3)!) = 8! / (3! * 5!).
Step 5: Calculate 8! = 8 × 7 × 6 × 5!, so we can simplify: C(8, 3) = (8 × 7 × 6) / (3 × 2 × 1).
