If they want a sample committee consisting of four male and four female students, from a possible volunteer pool of eight male and seven female students, how many ways can this committee be formed?

We can pick first the 4 man, and then the 4 women. The configuration of men and women are independant with each other, so the total of possibilities is obtained by multiplying the total possibilities to pick 4 men and the total possibilities of picking 4 women.

To pick 4 men from a group of 8, the total number of possibilities is the amount of ways to pick 4 elements from a group of 8. This number is represented by the combinatorial number of 8 with 4

[tex] {8 \choose 4} = \frac{8!}{4!4!} = 70 [/tex]

To pick 4 women from a group of 7, we need to count the total amount of ways to pick 4 elements from a group of 7. This is the combinatorial number of 8 with 7

[tex] {7 \choose 4} = \frac{7!}{4!3!} = 35 [/tex]

Hence, the total amount of ways to pick 4 men and 4 women from a group of 8 men and 7 women is 70*35 = 2450.