For this problem, assume 9 males audition, one of them being George, 6 females audition, one of them being Jackie, and 5 children audition. The casting director has 3 male roles available, 1 female role available, and 2 child roles available. How many different ways can these roles be filled if exactly one of George and Jackie gets a part?

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For this problem, assume 9 males audition, one of them being George, 6 females audition, one of them being Jackie, and 5 children audition. The casting director has 3 male roles available, 1 female role available, and 2 child roles available. How many different ways can these roles be filled if exactly one of George and Jackie gets a part?

Mathematics
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`if exactly one of George and Jackie gets a part` so they mean just one of them? either George OR Jackie? The wording they have is a bit odd
yes, i know the wording is odd

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I'm going to assume they meant to say George OR Jackie (exactly one person) gets the role. So it's not possible for both to get the role
`9 males audition` `3 male roles available` Let's say George is locked in to get a role. So we really have 3-1 = 2 slots left for the male roles. This is from a pool of 9-1 = 8 males how many ways are there to fill 2 slots from a pool of 8 males?
ok
56
order doesn't matter. So you divide 56 by 2 to get 28
okay but isnt it possible to have any of the three roles
I guess it depends on what the roles are. Are they important roles or extras? Hmm I'm not sure
if the roles are important (eg: leading roles), then order would matter since the characters are different
so then how do we account for the three roles he could play
I'm not sure now because I'm not sure what the roles are. So I don't know if order matters or not
Sorry I'm not really helpful with this one
well i have 4 attempts so lets do it with three separate roles on this
ok well if order did matter, then George could have male role A, male role B, male role C he has 3 choices if he picks male role A, then there are 8*7 = 56 ways to fill up the other 2 male roles if he picks male role B, then there are 8*7 = 56 ways to fill up the other 2 male roles if he picks male role C, then there are 8*7 = 56 ways to fill up the other 2 male roles as a shortcut, there are 3*56 = 168 ways to fill up the male roles assuming George gets a male role and order matters (the roles are important roles)
ok
how many ways are there to fill the female role? We're still under the assumption George got the role. So Jackie can't get the role if George did.
there is only 1 way if jackie gets the role
like I said ` We're still under the assumption George got the role. So Jackie can't get the role if George did.`
so what would the answer be
168?
we're not there yet how many ways are there to fill the female role? assume that Jackie can't get the role
6
jackie can't get the role though 6-1 = 5 so it's 5 actually
ah that makes sense
` 5 children audition` `2 child roles available.` how many ways to fill up these slots?
20
good
168*5*20 = 16800
summary so far IF george gets a role, then there are... 168 ways to fill up the male roles 5 ways to fill up the female role 20 ways to fill up the child roles
yes you beat me to it, you multiply those values out
that's just half the answer though
oh
we haven't considered the scenario that Jackie gets the role
give it a shot and tell me what you get
10080 if jackie gets the role
do we subtract them or add them together?
once again, if either Jackie or George gets the role, then the other person can't get it so we're now assuming Jackie gets the role. So george did NOT get the role. Try again
if george did NOT get the role, then the pool of 9 males drops to 8
sorry 6720
better
we have 2 cases George gets the role: 16800 different ways Jackie gets the role: 6720 different ways add them up
okay so that is 23520
yes
which is the final answer. It's the number of ways to pick all of the cast based on those specific conditions
it was the correct answer
:D
thanks man
ok so it was a lucky guess on our part to assume order mattered
no problem

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