probability

[M3LL]

6 sophmores, 10 juniors and 12 seniors are auditioning for parts in the high school play. how many ways can the order of their auditions be arranged if the seniors must all go first? if the first five students to audition must be seniors and the last five must be sophmores?

 

[JeffM]

6 sophmores, 10 juniors and 12 seniors are auditioning for parts in the high school play. how many ways can the order of their auditions be arranged if the seniors must all go first? if the first five students to audition must be seniors and the last five must be sophmores?

A good general way to attack hard problems in math is to break the problem up into parts that are easier. Some questions for you follow.

Take a simpler problem: how many ways are there to order the auditions of the 12 seniors? I presume that you know how to do that, right?

Now, for EACH way that you audition the seniors, how many ways are there to order the auditions of the 16 remaining students?. I presume you know how to do that, right?

So, how do you combine the answers to those two simpler questions to get the answer to your first problem?

Can you see a method of breaking up the second problem into simpler problems that you can do? [I warn you that the second problem is much harder.]