How many ways can a committee of 4 people be selected from a group of 10 people?
To answer this question, we can use the concept of combinations. The formula for calculating combinations is:
C(n, k) = n! / (k! * (n-k)!)
Where n is the total number of items, k is the number of items to be selected, and the exclamation mark (!) denotes factorial.
In this case, we need to calculate C(10, 4):
C(10, 4) = 10! / (4! * (10-4)!)
Now, let's break down the calculation step-by-step:
1. Calculate the factorial of 10:
10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3,628,800
2. Calculate the factorial of 4:
4! = 4 * 3 * 2 * 1 = 24
3. Calculate the factorial of (10-4):
(10-4)! = 6 * 5 * 4 * 3 * 2 * 1 = 720
4. Substitute these values back into the formula to find the number of ways:
C(10, 4) = 3,628,800 / (24 * 720) = 210
Therefore, there are 210 different ways to select a committee of 4 people from a group of 10 people.
C(10,4), or 10 choose 4
= 10!/(4!(10-4!)