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

Answer:

2,210,000 different schedules

Step-by-step explanation:

Cory needs to have an equal number of piano sonatas from J. S. Bach, Haydn, and Wagner.

Since he is setting up a schedule of 9 piano sonatas to be played, he needs:

• 3 out of 5 J. S. Bach piano sonatas
• 3 out of 52 Haydn piano sonatas
• 3 out of 5 Wagner piano sonatas

We then calculate how many different schedules are possible using combination.

Number of possible Schedules

$= ^5C_3 \times ^{52}C_3 \times ^5C_3\\=10 \times 22100 \times 10\\ =2210000 ways$

There are 2,210,000 different possible schedules.