An ice cream parlor has 33 different flavors. A super sundae allows a person to select 4 different flavors and 4 (out of 8) different toppings. How many different selections are possible?
A) 2,864,400
B) 971,890,920
C) 1,649,894,400
D) 68,745,600
E) 117,600

Question

An ice cream parlor has 33 different flavors. A super sundae allows a person to select 4 different flavors and 4 (out of 8) different toppings. How many different selections are possible? ​
A) 2,864,400
B) 971,890,920
C) 1,649,894,400
D) 68,745,600
E) 117,600

Quizplus · Accepted Answer

The number of ways to select 4 flavors out of 33 is given by the combination formula $C(n, k) = \frac{n!}{k!(n-k)!}$, where $n$ is the total number of items, and $k$ is the number of items to choose. So, for the flavors, it's $C(33, 4) = \frac{33!}{4!(33-4)!}$.For the toppings, since there are 8 to choose from and we want 4, it's $C(8, 4) = \frac{8!}{4!(8-4)!}$.The total number of different selections is the product of these two combinations: $C(33, 4) * C(8, 4)$.Calculating each:- $C(33, 4) = \frac{33!}{4!29!} = \frac{33 \times 32 \times 31 \times 30}{4 \times 3 \times 2 \times 1} = 40920$- $C(8, 4) = \frac{8!}{4!4!} = \frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1} = 70$Multiplying these together gives $40920 \times 70 = 2,864,400$.

An Ice Cream Parlor Has 33 Different Flavors