Question

In choosing what music to play at a charity fund raising event, Cory needs to have an equal number of piano sonatas from Mozart, Brahms, and Schubert. If he is setting up a schedule of the 6 piano sonatas to be played, and he has 18 Mozart, 3 Brahms, and 21 Schubert piano sonatas from which to choose, how many different schedules are possible?

Answer 1

Answer:

We conclude that have 96390 different schedules.

Step-by-step explanation:

We know that In choosing what music to play at a charity fund raising event, Cory needs to have an equal number of piano sonatas from Mozart, Brahms, and Schubert.  If he is setting up a schedule of the 6 piano sonatas to be played, and he has 18 Mozart, 3 Brahms, and 21 Schubert piano sonatas.  

We calculate  how many different schedules are possible:

$C_2^{18}\cdot C_2^3\cdot C_2^{21}=\frac{18!}{2!(18-2)!}\cdot \frac{3!}{2!(3-2)!}\cdot \frac{21!}{2!(21-2)!}=96390$

We conclude that have 96390 different schedules.