Question

You are trying to decide what to wear today. You take out 2 shirts, 2 pairs of pants, and 4 pairs of shoes that all

coordinate.
How many different outfits can be made with a shirt, a pair of pants, and a pair of shoes?

Answer 1

16

Explanation:

You can choose

• 1 pair of shoes in 2 different ways
• 1 pair of pants in 2 different ways
• 1 pair of shoes in 4 different ways

In total there are

`2\cdot 2\cdot 4=16`

different outfits.

Another way to solve this problem is simply count all outfits:

Shirts
`Sh_1, \ Sh_2`

Pants
`P_1,\ P_2`

Shoes
`S_1, \ S_2,\ S_3,\ S_4`

All outfits

`Sh_1P_1S_1, \\ Sh_1P_1S_2, \\ Sh_1P_1S_3, \\ Sh_1P_1S_4, \\ Sh_1P_2S_1, \\ Sh_1P_2S_2, \\ Sh_1P_2S_3, \\ Sh_1P_2S_4, \\ Sh_2P_1S_1, \\ Sh_2P_1S_2, \\ Sh_2P_1S_3, \\ Sh_2P_1S_4, \\ Sh_2P_2S_1, \\ Sh_2P_2S_2, \\ Sh_2P_2S_3, \\ Sh_2P_2S_4`