A fashion designer designs outfits for women with a blouse, skirt, and matching

Question

A fashion designer designs outfits for women with a blouse, skirt, and matching shoes. The shoes are always a matching pair. The blouse, skirt, and shoes are always a solid pattern featuring one of the seven colors of the rainbow (Red/Orange/Yellow/Green/Blue/lndigo/Violet). (a) How many outfits can the designer make (whether or not they match)? (b) A client wants the shoes to match cither the skirt or blouse, but not both. How many outfits can the designer offer? (c) A second client is happy with any outfit as long as the blouse, skirt and shoes are not all the same color (because that's boring). How many outfits can the designer offer?

Explanation / Answer

a)Each of the item can take one of the 7 colors.

Hence total number of ways=7*7*7=343 ways

b)Shoes should match either skirt or blouse but not both

Ways=(Shoes, Skirt same color)+(shoes,Blouse same color)-2*(shoes ,blouse,skirt same color)

(7*7)+(7*7)-2*(7)=84ways

c)All different=7*6*5=210ways

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