Questions: How many different committees can be formed from 7 teachers and 34 students if the committee consists of 2 teachers and 2 students? The committee of 4 members can be selected in different ways.

How many different committees can be formed from 7 teachers and 34 students if the committee consists of 2 teachers and 2 students?

The committee of 4 members can be selected in different ways.

Transcript text: How many different committees can be formed from 7 teachers and 34 students if the committee consists of 2 teachers and 2 students? The committee of 4 members can be selecthd in $\square$ different ways.

Solution

Solution Steps

Step 1: Calculate the number of ways to select teachers

To select 2 teachers out of 7 available, we use the combination formula $C(T, t) = \frac{T!}{t!(T-t)!}$. This gives us $C(7, 2) = \frac{7!}{2!(7-2)!} = 21$ ways.

Step 2: Calculate the number of ways to select students

To select 2 students out of 34 available, we use the combination formula $C(S, s) = \frac{S!}{s!(S-s)!}$. This gives us $C(34, 2) = \frac{34!}{2!(34-2)!} = 561$ ways.

Step 3: Calculate the total number of different committees

The total number of different committees that can be formed is the product of the number of ways to select teachers and students. This is $C(T, t) \times C(S, s) = 21 \times 561 = 11781$.