How many more ways can this be made?

Question

How many more ways can 10 jurors running for the positions of president, vice president, secretary, and treasurer be selected when compared to 12 sophomores running for 5 identical positions of class representative?

Answer 1

First consider how many ways of selecting 3 out of 10 jurors there are: 10×9×8/6=120. Then, having selected three, we have 3!=6 of placing these jurors into the three different posts. So 6×120=720 is the number of ways of selecting 3/10 jurors to the three posts.

Selecting 5 out of 12 sophomores: 12×11×10×9×8/5!=792. Since the posts have equal status we don't need to consider all possible arrangements of 5 posts.

So there are 792-720=72 more ways of selecting the sophomores than selecting the jurors (sophomore selection is 10% more than juror selection).