Question

Charlie has 4 pairs of shoes, 12 shirts, 5 pairs of pants, and 3 watches. How many days could he go without wearing the same combination of these four items?

Answer 1

Charlie can go 720 days without wearing the same combination of these four items

Explanation:

Each day Charlie is going to wear a pair of shoes, a shirt, a pair of pants and a watch.

So, for each pair of shoes, he can wear 12 shirts. For each shirt, he can wear 5 pair of pants. And for each pair of pants, he can wear a watch.

So, there are 5*3 = 15 possible combinations of watches and pants. For each one of these combinations, it can be worn with 12 shirts. So now there are 12*15 = 180 total combinations. Each one of these combinations can be worn with 4 pairs of shoes. So in all there are 720 total combinations, which means that Charlie can go 720 days without wearing the same combination of these four items.