Question

Your current wardrobe consists of eleven different items: three pairs of shoes, two pairs of pants, and six different shirts. Your mom offered to buy you a new shirt or a new pair of shoes. Which item (shoes or shirt) should your mom buy for you to maximize your total number of outfits (shoes-shirt-pant)?

Back of the book says shoes -48 outfits but I need the work

Answer 1

we will use basic counting princple, i.e. if one work can be done in A ways and second work can be done in B ways, then both works can be done in A*B ways

If mom buys 1 shirt, then total shirts(A) = 6+1 =7, total pants(B) = 2 and total shoes (C) = 3

By basic counting principle, number of outfits = A*B*C = 7*2*3 = 42 outfits possible

and

If mom buys 1 pair of shoes, then total shirts(A) = 6, total pants(B) = 2 and total shoes (C) = 3+1 = 4

By basic counting principle, number of outfits = A*B*C = 6*2*4 = 48 outfits possible

hence, buying a pair of shoes gives us 48 different outfits