Question

From a group of 6 juniors and 5 sophomores a committee of 3 juniors and 3 sophomores is to be selected. one junior is to receive a 12 month term on the committee, one junior is to receive a 9 month term, one junior is to receive a 6 month term and all sophomores are to receive 4 moth terms. How many different committees are possible?

Answer 1

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.

${n\choose k}=\frac{n!}{k!(n-k)!}$

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:

$n (3\ juniors)={6\choose 3}=\frac{6!}{3!(6-3)!}=\frac{6!}{3!\times3!}=\frac{6\times 5\times 4\times3!}{3!\times 3!}=20$

Compute the number of ways to select 3 sophomores from 5 as follows:

$n (3\ sophomores)={5\choose 3}=\frac{5!}{3!(5-3)!}=\frac{5!}{3!\times2!}=\frac{5\times 4\times3!}{3!\times 2!}=10$

Compute the total number of different committees possible as follows:

Total number of committees possible = n (3 juniors) × n (3 sophomores)

                                                               $={6\choose 3}\times {5\choose 3}\\=20\times 10\\=200$

Thus, the number of different committees that are possible is 200.