A large banana split consists of your choice of four scoops of ice cream, four dry toppings, and three wet top

Question

A large banana split consists of your choice of four scoops, four dry toppings and three wet toppings. The store has 28 flavors of ice crea, 26 dry toppings and 9 wet toppings. If you could eat one banana split every hour, how many hours would it take you to eat every possible combination of banana split with no repetitions?

Answer 1

Yum, now I'm hungry.

Ice cream:
From 28 choose 4:
28 x 27 x 26 x 25 / (4 x 3 x 2 x 1) = 20,475 ways

Dry toppings:
From 26 choose 4:
26 x 25 x 24 x 23 / (4 x 3 x 2 x 1) = 14,950 ways

Wet toppings:
From 9 choose 3:
9 x 8 x 7/ (3 x 2 x 1) = 84 ways

Total possible banana splits = 20475 * 14950 * 84 = 25,712,505,000

So it would tke you 25,712,505,000 hours to eat every possible combination.

Answer 2

i'm a purist. i like banana splits this form: 3 scoops of vanilla ice cream cradled between a sliced banana.. no longer green.. yet a severe high quality deep yellow... candy first scoop coated in strawberry sauce (with chunks) 2d scoop coated in chocolate syrup 0.33 scool coated in overwhelmed pineapple beneficiant dollops of whipped cream observed with chopped peanuts the surprising touch is the Marashino Cherry on appropriate of center scoop or all 3! Mmmmmm....

Answer 3

Use your basic product rule for independent decisions and the samplling without replacement, no regard to order:

ice cream, 28C4
dry , 26C4
wet, 9C3

Multiply those to get the number of combinations.

Jim's calculations are correct.

Answer 4

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