Question

Beethoven wrote 9 symphonies, Mozart wrote 27 piano concertos, and Schubert wrote 15 string quartets. (i) If a university radio station announcer wishes to play first a Beethoven symphony, then a Mozart concerto, and then a Schubert string quartet, in how many ways can this be done?

Answer 1

Answer:

This can be done in 3645 ways

Step-by-step explanation:

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

In this problem, we have that:

1 Beethoven symphony, from a set of 9.

1 Mozart concerto, from a set of 27.

1 string quartets, from a set of 15.

So

$P_{(9,1)}*P_{(27,1)}*P_{(15,1)} = \frac{9!}{(9-1)!}*\frac{27!}{(27-1)!}*\frac{15!}{(15-1)!} = 3645$

This can be done in 3645 ways