# how many different programs can a band have?

• Jul 12th 2009, 10:36 AM
morganfor
how many different programs can a band have?
If a band can play 30 classical pieces, 15 jazz pieces and 9 rock pieces and its program always consists of a classical followed by a jazz then a rock piece

A: how many different programs can it have?
I assume its just 30*15*9 right?

B: how many different programs are there if the pieces can be played in any order (but still only one piece from each category)

i'm kind of stuck on this part. do you have to divide by 3! because its a combination? but it seems like the answer should be larger than the first
• Jul 12th 2009, 08:50 PM
Arrangements
Hello morganfor
Quote:

Originally Posted by morganfor
If a band can play 30 classical pieces, 15 jazz pieces and 9 rock pieces and its program always consists of a classical followed by a jazz then a rock piece

A: how many different programs can it have?
I assume its just 30*15*9 right?

Correct!
Quote:

B: how many different programs are there if the pieces can be played in any order (but still only one piece from each category)

i'm kind of stuck on this part. do you have to divide by 3! because its a combination? but it seems like the answer should be larger than the first
Yes and no. Yes, the answer should be larger. No, you multiply by 3!, since this is the number of arrangements of 3 items.