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