thought this was a basic factorial question

[robo]

I'm trying to help my son on this, and darned if I didn't think I had this one...

"A panel of judges is to consist of 4 women and 5 men. A list of potential judges includes 7 women and 8 men. How many different panels could be created from this list?"

Well darn. I thought it was easy.

men = 8 possible, pick the first 5 so..... 8*7*6*5*4 = 6720
women = 7 possible, pick the first 4, so..... 7*6*5*4 = 840

add the 2, you get 7560. Except....that's not one of the choices.

GAH!!! Am I missing something far too easy or something? If I don't get how to do this one, then my son's entire factorial sheet is going to be wrong, because I must be missing a lot more than just this one. Gah! Help?!?!

 

[Unco]

G'day robo,

The order of the judges does not matter so we are dealing with combinations, not permutations.

In other words, you need to divide 6720 by 5! and 840 by 4! to get the number of ways where the order does not matter.

Also, the men and women are being selected at the same time (they are not separate events) so you need to multiply the two numbers, not add.

 

[robo]

wow, son of a gun. thanks.

hurm....how do I know when to divide by 4! and 5! ?

obviously it's the # of choices, but...when do I divide and when do I not?

thanks a bunch.

 

[robo]

for example...

"A committee is to consist of 4 members. There are 6 men and 4 women available to serve on the comittee, how many different committees can be formed?"

So obviously, the committee is "asexual", so essentially, 4 members, 10 choices.

10*9*8*7 was my first response (5040)

but should it actually be (10*9*8*7) / 4! = 210?

sorry about the obvious questions, but it has been a good 17 or so years since I've even THOUGHT about this stuff. Oy!! much rust to wipe away!!!

Thanks.

 

[Unco]

G'day robo,

wow, son of a gun. thanks.

hurm....how do I know when to divide by 4! and 5! ?

obviously it's the # of choices, but...when do I divide and when do I not?

thanks a bunch.

Divide when you know the order doesn't matter. Selecting people to join a committee, selecting vegetables to put on a plate, etc. the order doesn't matter.

"A committee is to consist of 4 members. There are 6 men and 4 women available to serve on the committee, how many different committees can be formed?"

So obviously, the committee is "asexual", so essentially, 4 members, 10 choices.

10*9*8*7 was my first response (5040)

but should it actually be (10*9*8*7) / 4! = 210?

But you said there were 10 choices! Just kidding... As I said above (I used the committee example before reading your other post), the order doesn't matter so divide by 4!. Correct.