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 which is
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 which is ways for the toppings, so
(80730)(70) = 5651100 ways for ice cream and toppings.
Edwin