Answer:
The number of possible outfits Dustin can wear is 73 outfits
Step-by-step explanation:
The information given are;
The number of hats Dustin has = 5
The number of shirts Dustin has = 5
The number of pants Dustin has = 5
The number of shoes Dustin has = 5
The colors of Dustin's clothing are blue, green, gray, silver, and gold
Given that the shoes go with at least two other clothing of the same color, we have;
The number of ways the color of the shoes can be selected = 5 ways
The number of ways of selecting the same color for 2 of the remaining 3 clothing = 3 ways
The number of ways of selecting the color of the fourth clothing = 5 ways
The total number of ways = 5 × 3 × 5 = 75 ways
The number of ways in which all silver can be selected = 1 way
The number of ways in which all gold can be selected = 1 way
Since Dustin refuses to wear all silver and all gold, the total number of ways the outfits can be selected = 75 - 1 - 1 = 73 ways = 73 is the number of possible outfits
Therefore, the number of possible outfits Dustin can wear = 73 outfits.
