Question

In choosing what music to play at a charity fund raising event, Cory needs to have an equal number of piano sonatas from J. S. Bach, Haydn, and Wagner. If he is setting up a schedule of the 9 piano sonatas to be played, and he has 5 J. S. Bach, 52 Haydn, and 5 Wagner piano sonatas from which to choose, how many different schedules are possible

Answer 1

Cory can create 0 different schedules for the charity fund raising event, as he cannot fulfill the requirement to have an equal number of piano sonatas from each composer with the available options.

Step-by-step explanation:

Cory needs to set up a schedule of 9 piano sonatas with an equal number from three composers: J. S. Bach, Haydn, and Wagner. There will be 3 sonatas from each composer in the schedule. Since Cory has 5 Bach sonatas, he can choose 3 of these in 5 choose 3 ways (10 ways), for Haydn, he has plenty to choose from, but it's still 52 choose 3 ways, and for Wagner, similarly to Bach, it's 5 choose 3 ways. Therefore, the number of different schedules possible is the product of these individual choices. The calculation is:

1. 
   
3. Calculate the number of ways to choose 3 Bach sonatas from 5: C(5,3) = 5! / (3!(5-3)!) = 10
4. 
   
6. Calculate the number of ways to choose 3 Haydn sonatas from 52: C(52,3)
7. 
   
9. Calculate the number of ways to choose 3 Wagner sonatas from 5: C(5,3) = 10
10. 
    
12. Multiply the results to find the total number of schedules: 10 * C(52,3) * 10

We don't need to calculate C(52,3) as it doesn't affect the unique count when multiplied by zero from other terms. The total number of different schedules is then 0, as either the Bach or the Wagner choices eliminate all possibilities.