SOLUTION: At the ice cream shop, there are 27 flavors of ice cream available. How many ways can you select a bowl of 5 scoops of ice cream if each scoop is a different flavor? Your answer

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Question 1184518: At the ice cream shop, there are 27 flavors of ice cream available. How many
ways can you select a bowl of 5 scoops of ice cream if each scoop is a
different flavor?
Your answer is :

The ice cream shop has 8 types of toppings available, and you decide to add
4 toppings to your bowl of 5 scoops of ice cream. How many combinations of 5
scoops of ice cream and 4 toppings are possible?
Your answer is :

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
At the ice cream shop, there are 27 flavors of ice cream available. How many
ways can you select a bowl of 5 scoops of ice cream if each scoop is a
different flavor?
We will assume that the order in which the flavors are arranged in the bowl
doesn't matter, so it's COMBINATIONS, not PERMUTATIONS.

The COMBINATIONS of 27 flavors taken 5 scoops at a time is 27C5 or C(27,5)
or 27C5 or 27C5 or %28matrix%282%2C1%2C27%2C5%29%29 which is

%2827%2A26%2A25%2A24%2A23%29%2F%285%2A4%2A3%2A2%2A1%29=80730 ways.

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The ice cream shop has 8 types of toppings available, and you decide to add
4 toppings to your bowl of 5 scoops of ice cream. How many combinations of 5
scoops of ice cream and 4 toppings are possible?
For each of those 80730 ways to have 5 flavors, there are all the
COMBINATIONS of 8 toppings taken 4 at a time, which is 8C4 or C(8,4)
or 8C4 or 8C4 or %28matrix%282%2C1%2C8%2C4%29%29 which is %288%2A7%2A6%2A5%29%2F%284%2A3%2A2%2A1%29=70 ways for the toppings, so 
(80730)(70) = 5651100 ways for ice cream and toppings.

Edwin