How many ways can 9 performances at a piano recital be ordered?

To determine the number of ways 9 performances at a piano recital can be ordered, we can calculate the number of permutations of 9 items. The formula for the number of permutations of n items is given by:

Number of Permutations = n!

where n! represents the factorial of n, which is the product of all positive integers up to n.

In this case, n = 9, so the number of permutations for 9 performances is:

Number of Permutations = 9!

Calculating 9! by multiplying all the integers from 1 to 9, we get:

9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880

Therefore, there are 362,880 ways that 9 performances at a piano recital can be ordered.