Question

In choosing what music to play at a charity fund raising event, Davon needs to have an equal number of string quartets from Mendelssohn, Schubert, and Rubinstein. If he is setting up a schedule of the 6 string quartets to be played, and he has 6 Mendelssohn, 15 Schubert, and 10 Rubinstein string quartets from which to choose how many different schedules are possible?

Answer 1

To determine the number of possible schedules for Davon's event, calculate combinations for choosing 2 quartets from each composer's available works and then multiply these together. This results in 70,875 possible schedules.

Step-by-step explanation:

Davon needs to select an equal number of string quartets from Mendelssohn, Schubert, and Rubinstein to play at a charity fundraising event. He can choose from 6 Mendelssohn, 15 Schubert, and 10 Rubinstein string quartets and needs to set up a schedule of 6 string quartets to be played in total.

To have an equal number of quartets from each composer, Davon must choose 2 quartets from each composer since 6 quartets divided equally among 3 composers gives us 2 quartets per composer.

The number of different schedules possible can be calculated by multiplying the number of ways to choose 2 quartets from each group of composers' works. For Mendelssohn, that's 6 choose 2; for Schubert, that's 15 choose 2; and for Rubinstein, that's 10 choose 2.

Using the combination formula where nCk = n! / (k! (n - k)!), we get:

Mendelssohn: 6C2 = 6! / (2! (6 - 2)!) = 15
Schubert: 15C2 = 15! / (2! (15 - 2)!) = 105
Rubinstein: 10C2 = 10! / (2! (10 - 2)!) = 45

The total number of different schedules is the product of these numbers: 15 * 105 * 45 = 70,875 possible different schedules for the event.