Question

A pianist plans to play 4 pieces at a recital from her repertoire of 20 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

There are 1,16,280 different recital programs possible.

Given: A pianist plans to play 4 pieces at a recital from her repertoire of 20 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:-

$^{n} P_{r} =\frac{n!}{(n-r)!}$

Now, the number of different recital programs are:-

$^{20} P_{4} =\frac{20!}{(20-4)!}=\frac{20*19*18*17*16!}{16!}=116280$

Hence, there are 1,16,280 different recital programs possible.

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