Answer: For a medium sundae, the problem tells us the scoops can be the same or different. If the two scoops are different flavors, there
are 5C2 = 5!/(2! × 3!) = (5 × 4)/(2 × 1) = 10 possibilities. If the two scoops are of the same flavor, there are 5 possibilities, one
for each of the five flavors. For the toppings there are three choices, therefore, for a medium sundae there are (10 + 5) × 3 =
15 × 3 = 45 combinations. Similarly, for three scoops of all different flavors, there are 5C3 = 5!/(3! × 2!) = (5 × 4)/(2 × 1) =
10 possibilities. For three scoops with two or three scoops of the same flavor, there 5 double scoops to choose from and 5 single
scoops to choose from giving 5 × 5 = 25 possibilities. To choose the two toppings, there are 3C2 = 3!/(2! × 1!) = 3 possibilities.
So, the total number of large sundae combinations is (10 + 25) × 3 = 35 × 3 = 105 combinations. In total, at Moo’s ice cream
shop, there are 15 + 45 + 105 = 165 ice cream sundae combinations.
Step-by-step explanation: