Question

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

Answer 1

10 juniors are running for 4 positions.
There are ten people who can get into the first spot
Nine people for the second
8 people for the third
7 for the fourth
10x9x8x7= 5040 different ways.

For the sophomores: 12x11x10x9x8= 95040
However, the positions are identical which means that the order doesn't matter. (There's a difference between A getting postion 1, B for 2, C for 3, D for 4 and B for 1, A for 2, C for 3, D for 4)

There are 5 identical positions, therefore we divide this by 5! (5x4x3x2x1)= 120
95040/120= 792
Juniors have 5040 positions, sophomores have 792