Questions: A pianist plans to play 6 pieces at a recital. In how many ways can she arrange these pieces in the program?

Transcript text: A pianist plans to play 6 pieces at a recital. In how many ways can she arrange these pieces in the program?

Solution

Solution Steps

To determine the number of ways the pianist can arrange 6 pieces, we need to calculate the number of permutations of 6 distinct items. This is given by the factorial of 6, denoted as \(6!\).

Step 1: Determine the Number of Arrangements

To find the number of ways to arrange 6 distinct pieces, we calculate the factorial of 6, denoted as \(6!\). The factorial function is defined as the product of all positive integers up to that number.

Step 2: Calculate \(6!\)

The calculation for \(6!\) is as follows: \[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \]