Selecting a Panel

[fschneider13]

Hello,

I took the CAT #1, and I would like to ask more information about this question:

A certain panel is to be composed of exactly three women and exactly two men, chosen from x women and y men. How many different panels can be formed with these constraints?

(1) If two more women were available for selection, exactly 56 different groups of three women could be selected.

(2) x = y + 1

I’m not sure how is it possible to figure out this explanation: "One concept that you need to know for the exam is that when dealing with combinations and permutations, each result corresponds to a unique set of circumstances. For example, if you have z people and know that choosing two of them would result in 15 different possible groups of two, it must be true that z = 6. No other value of z would yield exactly 15 different groups of two. So if you know how many subgroups of a certain size you can choose from an unknown original larger group, you can deduce the size of the larger group."

How is it possible to find "n" having only the total of groups and "r" ?

Could you help me?

Tks

[jnelson0612]

Hello,

I took the CAT #1, and I would like to ask more information about this question:

A certain panel is to be composed of exactly three women and exactly two men, chosen from x women and y men. How many different panels can be formed with these constraints?

(1) If two more women were available for selection, exactly 56 different groups of three women could be selected.

(2) x = y + 1

I’m not sure how is it possible to figure out this explanation: "One concept that you need to know for the exam is that when dealing with combinations and permutations, each result corresponds to a unique set of circumstances. For example, if you have z people and know that choosing two of them would result in 15 different possible groups of two, it must be true that z = 6. No other value of z would yield exactly 15 different groups of two. So if you know how many subgroups of a certain size you can choose from an unknown original larger group, you can deduce the size of the larger group."

How is it possible to find "n" having only the total of groups and "r" ?

Could you help me?

Tks

Just to clarify before I answer, you mean that n is the population and r is the number being selected?

[fschneider13]

Yes.

Tks.

[tim]

This boils down to an algebra problem. If you select r from a group of n and there are x ways to do that, the formula looks like this:

n!/(r!(n-r)!) = x

Since you have stipulated that we know r and x, just plug those numbers in and you'll end up with an equation with only a single variable n that you can then solve.