Combinatorics You have 3 tshirts 5 pairs of shorts and 2 pai

(Combinatorics) You have 3 t-shirts, 5 pairs of shorts, and 2 pairs of shoes. You want to go to the beach but the sign says \"No shirt, no shoes, no service,\" (note that it does not say \"no shorts.\") You are eccentric so you don\'t care if your shoes match (although you can\'t wear a shoe for your right foot on your left and vice-versa, but you can mismatch the two pairs.) How many different outfits can you wear to the beach? (also note this is not a trick question, simply one of counting principles). Please show your work and final answer.

Solution

ONE OUT OF THREE T SHIRTS ONE OUT OF TWO SHOES IN RIGHT LEG AND ONE OUT OF TWO IN LEFT

AND YU CAN EITHER WEAR A SHORT OR DOESN\'T WEAR.

SO

3 choose 1 * 2 choose 1 * 2 choose 1 * (5 choose 1 + 5 choose 0) = 72 ways