There are 3 people who are chosen to serve on a comitee out of a group of 3 girls and 4 boys. How many different committees can be formed?
Mathematics · Middle School · Tue Nov 03 2020
Answered on
To determine the number of different committees that can be formed with 3 people chosen from a group of 3 girls and 4 boys, you can use combinations.
The formula for combinations is \(C(n, k) = \frac{n!}{k!(n-k)!}\), where \(n!\) denotes the factorial of \(n\), and \(k\) is the number of elements to be chosen.
In this case, you want to choose 3 people from a group of 7 (3 girls + 4 boys), so the calculation is:
\[C(7, 3) = \frac{7!}{3!(7-3)!}\]
\[C(7, 3) = \frac{7!}{3! \times 4!}\]
\[C(7, 3) = \frac{7 \times 6 \times 5}{3 \times 2 \times 1}\]
\[C(7, 3) = 35\]
So, there are 35 different committees that can be formed with 3 people chosen from the group of 3 girls and 4 boys.