Question

25 people apply for a job, 15 men and 10 women. they will hire 10 people, with 40% of them women. how many different staff selections are possible?

Answer 1

So if they'll hire 40% women, and they're hiring 10 people, this means that they'll hire 4 women. And the rest of the people are all men, or 6 of them. 

So basically, you can think of this like a tree, taking the men's side first, with 15 possible hires in the beginning, and then 14 more stemming off of that, and then 13 more stemming of those, etc.

So basically it would be:

15 * 14 * 13 * 12 * 11 * 10

Because there are four spots for men, and there were 15 men, and after every hire, there will be one less applicant, because there would've been one hire instead.

So;

15 * 14 * 13 * 12 * 11 * 10 = 3603600

And then women just do the same thing.

10 * 9 * 8 * 7 = 5040

Then just multiply those together as well.

18162144000 is your final answer.