A total of 8 representatives need to be chosen from a group of 40 students, of which 24 are female and 16 are male. In how many ways can this be done? What if we require that there be at least 3 female and 3 male representatives?

To find this, we need to know the number of ways the representatives can be picked overall, and then the number of ways 3 females and 3 males can be the representatives. The fraction of the two will be the probability.

The total number of ways the representatives can be picked is the combination of a pool of 40 students and choosing 8 is; C(40,8) = 40!/((8!)(40 - 12)!)

= 76904685

We have gotten the number of ways the representatives can be picked.

Now let's find how many ways can the jury consist of 3 females and 3 males

For the males, there are 16 in the pool and we're picking 3:

Thus, C(16,3) = 16!/((3!)(16 - 3)!) = 560

For the females, there are 24 in the pool and we're picking 3:

Thus, C(24,3) = 24!/((3!)(24 - 3)!) = 2024

Thus, number of men and women choices = 2024 x 560 = 1133440

So; probability = 1133440/76904685 = 0.0147