Questions: A pianist plans to play 5 pieces at a recital from her repertoire of 21 pieces, and is carefully considering which song to play first, second, etc. to create a good flow. How many different recital programs are possible?

Solution Steps

The pianist has a total of \( 21 \) pieces in her repertoire.

The pianist plans to play \( 5 \) pieces at the recital.

To find the number of different recital programs, we use the permutation formula:

\[ P(n, r) = \frac{n!}{(n - r)!} \]

where \( n \) is the total number of pieces and \( r \) is the number of pieces to be played. Substituting the values:

\[ P(21, 5) = \frac{21!}{(21 - 5)!} = \frac{21!}{16!} = 21 \times 20 \times 19 \times 18 \times 17 = 2441880 \]

Final Answer