Question

A pianist plans to play 4 pieces at a recital from her repertoire of 23 pieces, and is carefully considering which song to play first, second, etc. to create a good flow. How many different recital programs are possible?

Answer 1

Answer: 212,520

Step-by-step explanation:

Given : A pianist plans to play 4 pieces at a recital from her repertoire of 23 pieces, and is carefully considering which song to play first, second, etc.

It means the repetition of pieces is not allowed.

When repetition is not allowed , then the number of ways to arrange n things where r things taken together is given by :-

$^nP_r=\dfrac{n!}{(n-r)!}$

Now, the number of different recital programs are :-

$^{23}P_4=\dfrac{23!}{(23-4)!}=\dfrac{23\times22\times21\times20\times19!}{19!}=212,520$

Hence, there are 212,520 different recital programs possible.