Respuesta :
Answer:
The number of different committees that are possible is 200.
Step-by-step explanation:
Combinations is a mathematical procedure to determine the number of ways to select k items from n distinct items.
[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]
The group consists of 6 juniors and 5 sophomores.
The committee to be formed must consist of 3 juniors and 3 sophomores.
Compute the number of ways to select 3 juniors from 6 as follows:
[tex]n (3\ juniors)={6\choose 3}=\frac{6!}{3!(6-3)!}=\frac{6!}{3!\times3!}=\frac{6\times 5\times 4\times3!}{3!\times 3!}=20[/tex]
Compute the number of ways to select 3 sophomores from 5 as follows:
[tex]n (3\ sophomores)={5\choose 3}=\frac{5!}{3!(5-3)!}=\frac{5!}{3!\times2!}=\frac{5\times 4\times3!}{3!\times 2!}=10[/tex]
Compute the total number of different committees possible as follows:
Total number of committees possible = n (3 juniors) × n (3 sophomores)
[tex]={6\choose 3}\times {5\choose 3}\\=20\times 10\\=200[/tex]
Thus, the number of different committees that are possible is 200.
