Question

Robin has five t-shirts of different colors, three pairs of shorts of different patterns, and four pairs of shoes of different colors. She is planning a trip to the beach. In how many ways can she combine these items if

a.) The orange t-shirt clashes with the red shorts?

b.) The red t-shirt clashes with the striped shorts?

Answer 1

a) Given that orange t-shirt clashes with the red shorts, we cannot use those 2 together.

Total number of combinations with orange t-shirt and red shorts is computed here as:
= number of different pair of shoes possible
= 4

Total # of combinations of the 3 things here is computed as:
= 5*3*4 = 60

Therefore total combinations allowed = 60 - 4 = 56

Therefore in 56 ways the elements could be combined here.

b) We are given the red t-shirt clashes with the striped shorts, therefore the number of combinations here would be same as above part ( because of same kind of constraint here )

Therefore in 56 ways the elements could be combined here.