[Guest]

president, secretary, and treasurer, if the president and treasurer must be women N={alan bill david cathy dave evelyn] how many posibilities?

Edited February 24, 2009 by martin1

[Guest]

Are you asking me to do homework, or explain something? There are bajillions of examples of people doing probability on this site, if you want to find them, but I guess I'll explain a little of the methodology here...

You know that the president and treasurer must be women, and the secretary has no restrictions. Therefore, the first step is to figure out how many ways there are for the president and treasurer to be women. From the look of it you have 2 women, so that should be easy (you won't have an extra woman to complicate matters for the other position). After that, the next step is to figure out how many ways you can fill the remaining spots, or in this case, spot. Take the number of ways to fill the first requirement, multiply it by the number of ways to fill the remainder of the positions (assuming the first requirement has been filled), and then divide by the total number of ways any of the positions could be filled.

This is a small enough sample set to just brute force the answer, which would be the way I'd do it (just list all the possibilities, then figure out which ones satisfy your criteria), as the "real" answer involves a good deal of multiplication.

[Prime]

president, secretary, and treasurer, if the president and treasurer must be women N={alan bill david cathy dave evelyn] how many posibilities?

The method for calculating the number of possibilities is straightforward.

1. Arrange the positions to be filled in any order you like. For example: President, Treasurer, Secretary.

2. For each position see in how many ways you can fill it with the remaining people.

3. Multiply all the numbers thus obtained.

[Guest]

president, secretary, and treasurer, if the president and treasurer must be women N={alan bill david cathy dave evelyn] how many posibilities?

Careful how you phrase your questions. The sticky above says, "Make it clear what it is about your homework you don't understand." All you've done in your OP is posted a homework question and a post has already been removed for giving the answer.

[Guest]

But of course! I love to count!

This is a very small set, as mentioned above, so yes, you should brute force this, as I think it would be easier to do so rather than using actuall counting methods.

But as this has already been mentioned, I must contribute!

Counting is very important, and very easy. This is a permutations problem, not combination, so I will provide.

_nP_r= n!/ (n-r)!

Memorize!

How to apply: the P thingy means how many permutations with the given things. _nP_r is how many permutations of r numbers you can get out of a set of n.

An actual application: If there are 15 people, and everyone wishes to give everyone else a gift, how many gifts will be exchanged?

Well, this is a less obvious permutations problem, but you can use this method if you wish. A gift is exchanged between two people, no less, no more. Everyone gives a gift to everyone else, because this is a math problem, and everyone is nice. The answer is ₁₅P₂ ( usually when writing blahPblah, blah is in subscipts.) which is equal to 15!/13!. Not as a monstrosity as you might imagine. It simplifies to 15*14, or 210 gifts exchanged.

If you don't know what ! means, I can't help you because you haven't been learning.

But just if you wish to research, it means factorial.

Oh, and please use proper spelling and grammer, as well as proper punctuation. The fact that the mentioned was mangled so badly was the only reason the previous paragraph was written.

Edited February 13, 2010 by new guest

[MissKitten]

this is actually kind of easy.

so, lets say you have 5 people: 3 male and 2 female. you need a comittee of 3 people, and at least one has to be female. all you do is see how many people you can have in each spot and multiply, like this:

2 * 4 * 3 = 24

you get the first '2' because at least one person has to be female. you get the second '4' because after you choose the first person, you only have 4 people remaining. and you get the third '3' because after you choose the first and second people, you have only 3 people remaining. just apply the same thing to your problem. the permutation formula would work here too, but personally, i find it really confusing.

i hope i was able to help.