Problem

An ice cream parlor offers 30 different flavors of ice cream. One of its items is a bowl consisting of three scoops of ice cream, each a different flavor. How many such bows are possible?

There are bowls of three-flavor ice cream possible.

Answer

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Answer

Final Answer: There are \(\boxed{4060}\) bowls of three-flavor ice cream possible.

Steps

Step 1 :We are given that an ice cream parlor offers 30 different flavors of ice cream. One of its items is a bowl consisting of three scoops of ice cream, each a different flavor. We are asked to find out how many such bowls are possible.

Step 2 :This is a combination problem. We are choosing 3 flavors out of 30, and the order in which we choose the flavors does not matter.

Step 3 :The formula for combinations is: \[C(n, k) = \frac{n!}{k!(n-k)!}\] where n is the total number of items, k is the number of items to choose, and '!' denotes factorial. In this case, n=30 and k=3.

Step 4 :Substituting the given values into the formula, we get: \[C(30, 3) = \frac{30!}{3!(30-3)!}\]

Step 5 :Solving the above expression, we find that the number of combinations is 4060.

Step 6 :Final Answer: There are \(\boxed{4060}\) bowls of three-flavor ice cream possible.

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