Question

How do you solve it?

Lorena is the administrator of a store selling shoes for women and 12 different models arrive this summer.

If you want to place 4 pairs of shoes per shelf in the store, how many ways can you organize them?

A) 28
B)495
C)11880
D)20736
E) 20

Answer 1

I believe the answer is C) 11 880 ways, if we consider order on the shelf to matter.

Explanation:

You treat each pair of shoes as a single object. In that case, you have 12 items and you will choose 4, with order being important (the way I am reading the problem at least).

So, we calculate the permutations of 12 objects, taking 4 at a time:

12P4 = `12!/(12-4)! = 12xx11xx10xx9 = 11 880` ways.

(By the way, if you consider order not to be important, then we calculate a combination of 4 chosen from 12 items, which is

12C4 = `(12!)/((12-4)!4!) = 495` ways)