Understanding Combinations
This problem involves combinations because the order in which Dana chooses the mice doesn't matter. Choosing mouse #1 then mouse #2 then mouse #3 is the same as choosing mouse #3 then mouse #1 then mouse #2.
The Formula
The number of ways to choose *r* items from a set of *n* items (where order doesn't matter) is given by the following formula:
* nCr = n! / (r! * (n-r)!)
Where:
* nCr represents the number of combinations
* n! means n factorial (n * (n-1) * (n-2) * ... * 2 * 1)
Applying the Formula
In this case:
* n = 9 (total number of mice)
* r = 3 (number of mice Dana wants to buy)
So, the number of ways Dana can choose 3 mice is:
* 9C3 = 9! / (3! * (9-3)!)
* = 9! / (3! * 6!)
* = (9 * 8 * 7 * 6!)/(3 * 2 * 1 * 6!)
* = (9 * 8 * 7) / (3 * 2 * 1)
* = 84
Answer: Dana can choose 3 mice in 84 different ways.