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?
<pre>
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 <sub>27</sub>C<sub>5</sub> or <sup>27</sup>C<sub>5</sub> or {{{(matrix(2,1,27,5))}}} which is

{{{(27*26*25*24*23)/(5*4*3*2*1)=80730}}} ways.</pre>  
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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?<pre>
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 <sub>8</sub>C<sub>4</sub> or <sup>8</sup>C<sub>4</sub> or {{{(matrix(2,1,8,4))}}} which is {{{(8*7*6*5)/(4*3*2*1)=70}}} ways for the toppings, so 
(80730)(70) = 5651100 ways for ice cream and toppings.

Edwin</pre>