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Chapter 5: Problem 42

An ice cream shop offers 25 flavors of ice cream. How many ways are there to select 2 different flavors from these 25 flavors? How many permutations are possible?

Short Answer

Expert verified
There are 300 ways to select 2 different flavors from the 25 and 600 permutations possible.

Step by step solution

01

Understanding combinations

In mathematics, a combination refers to a selection of items without considering the order. So if we need to choose 2 flavors of ice cream from 25, we use the combination formula which is defined as: \[ C(n, k) = \frac{n!}{k!(n-k)!} \] Where 'n' stands for the total number of items and 'k' stands for the number of items to choose. '!' denotes factorial, which means the product of all positive integers less than or equal to that number.
02

Calculate combinations

To calculate the combinations substitute 'n' with 25 (total number of flavors) and 'k' with 2 (number of flavors to choose). \[ C(25, 2) = \frac{25!}{2!(25-2)!} \] After simplification the answer is 300.
03

Understanding permutations

A permutation refers to the arrangement of items in a particular order. When selecting 2 flavors from 25, the order in which they are selected creates different permutations. The formula for permutations is defined as: \[ P(n, k) = \frac{n!}{(n-k)!} \] Where 'n' stands for the total number of items and 'k' stands for the number of items to arrange.
04

Calculate permutations

To calculate the permutations substitute 'n' with 25 (total number of flavors) and 'k' with 2 (number of flavors to choose). \[ P(25, 2) = \frac{25!}{(25-2)!} \] After simplification the answer is 600.

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