Question

how many different 12 member juries can be chosen from a pool of 35 people?

Answer 1

After you pick from the pool of 35 there will be only 34 left. So we have 35 choices for the first and 34 for the next, etc... So we can write it out as multiplication like this:

35*34*33*...*23

since
23=35-12.

However this isn't the end of it. This considers that these twelve people are organized so that the order that we pick them in matters, but it doesn't. So we need to divide out that many people, which is 12 factorial.