Wide Variety Of Flavors
An ice cream parlor has 6 flavors of ice creams. If you can have 3 scoops on a cone (where the flavors are not necessarily distinct and the order matters: bottom, middle, top), the number of all possible variations of your ice cream will be . Now, what would the number of variations if, this time, the three scoops must all be distinct flavors and the order of the three flavors still matters?
The answer is 120.
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1 solution
For the first scoop, there are 6 flavors we can use. Next, for the second scoop, there are only 5 flavors we can use, because three scoops must all be distinct flavors and there is a flavor that we have already used for the first scoop. Finally, the third scoop, the same as the second scoop, there are 4 flavors for it. Thus, there are 6 × 5 × 4 = 1 2 0 variations for this delicious ice cream.