You are trying to decide what to wear today. You take out 2 shirts, 2 pairs of pants, and 4 pairs of shoes that allcoordinate.How many different outfits can be made with a shirt, a pair of pants, and a pair of shoes?

Accepted Solution

Answer:16Step-by-step explanation:You can choose1 pair of shoes in 2 different ways1 pair of pants in 2 different ways1 pair of shoes in 4 different waysIn total there are [tex]2\cdot 2\cdot 4=16[/tex]different outfits.Another way to solve this problem is simply count all outfits:Shirts [tex]Sh_1, \ Sh_2[/tex]Pants [tex]P_1,\ P_2[/tex]Shoes [tex]S_1, \ S_2,\ S_3,\ S_4[/tex]All outfits[tex]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[/tex]