In how many words can a committee of 5 people be chosen out of 8 people
8P5 = 8*7*6*5*4
You may not care about order withing each committee so perhaps you mean combinations, not permutations
C(8,5) = 8! /[ 5! (8-5)! ]
= 8*7*6/[3*2]
= 56
To find out how many words can be formed by choosing a committee of 5 people out of 8 people, we can use the concept of combinations.
The number of ways to choose a committee can be calculated using the formula for combinations, which is:
C(n, r) = n! / (r! * (n-r)!)
Where:
- C(n, r) represents the number of combinations of n items taken r at a time.
- n! denotes the factorial of n, which is the product of all positive integers up to n.
In this case, we want to choose a committee of 5 people out of a total of 8 people. So, applying the formula:
C(8, 5) = 8! / (5! * (8-5)!)
= 8! / (5! * 3!)
Now, let's simplify the equation:
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
5! = 5 * 4 * 3 * 2 * 1
3! = 3 * 2 * 1
Plugging in these values:
C(8, 5) = (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / ((5 * 4 * 3 * 2 * 1) * (3 * 2 * 1))
= (8 * 7 * 6) / (3 * 2 * 1)
Now, let's calculate the resulting fraction:
C(8, 5) = (8 * 7 * 6) / (3 * 2 * 1)
= 336 / 6
= 56
Therefore, there are 56 ways to choose a committee of 5 people out of 8 people.