how many different four person committees can be formed from a group of five boys and four girls
9 people to choose from, so 9C4
To find the number of different four-person committees that can be formed, we can use the concept of combinations. The formula for combinations is:
C(n, k) = n! / (k!(n-k)!)
Where
- n is the total number of objects (in this case, the total number of people)
- k is the number of objects we want to choose (in this case, the number of people in each committee)
- ! denotes factorial, which means multiplying a number by all positive integers less than it down to 1.
In this case, we want to choose four people from a group of five boys and four girls. The total number of people, n, is 5 boys + 4 girls = 9 people. We want to choose 4 people, so k = 4.
Substituting these values into the formula, we have:
C(9, 4) = 9! / (4!(9-4)!)
= 9! / (4!5!)
Calculating the factorial values:
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
4! = 4 x 3 x 2 x 1
5! = 5 x 4 x 3 x 2 x 1
Now we can simplify the formula:
C(9, 4) = (9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / ((4 x 3 x 2 x 1) x (5 x 4 x 3 x 2 x 1))
After canceling out common terms in the numerator and denominator, we get:
C(9, 4) = (9 x 8 x 7 x 6) / (4 x 3 x 2 x 1)
= 3024 / 24
= 126
Therefore, there are 126 different four-person committees that can be formed from a group of five boys and four girls.