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- July 22nd 2009, 05:17 AM #1

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## combinatorices

Hello, I have a small question please...

In a building there are 8 floors, in each floor, there are 4 flats. In each flat lives a couple ( man & woman ). We want to choose committee of 4 people ( a family can send only 1 representative ). What is the probability that the committee will contain 4 women ?

( assume that the chances of choosing men and women are equal )

thankes!

- July 22nd 2009, 05:56 AM #2

- July 22nd 2009, 06:00 AM #3

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The number of flats is irrelevant.

You choose 4 flats to the committee, all the flats are equal so it doesnt matter how many there are.

Of those flats you choose a man or a woman in each.

you can make different groups and only 1 all women group so the chance is 1/16.

edit:sorry I didnt noticed someone had already answered

- July 22nd 2009, 06:13 AM #4

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- July 22nd 2009, 06:21 AM #5

- July 22nd 2009, 08:22 AM #6

- July 22nd 2009, 08:37 AM #7

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- July 22nd 2009, 09:37 AM #8
There are ways the select the committee.

There are ways the select the committee of all women.

We pick the four flats. Take the lady from each of the flats.

That gives .

As was pointed out by Haytham, the number of flats does not matter (it does have to be at least four).

Once the four flats a chosen, we can pick either wife or husband. That is ways.

- July 22nd 2009, 12:22 PM #9

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now I got it, thanks ! it does not matter the number of flats...

I have just found out an addition to the question, I hope you don't mind....

b. what is the probability of all people in the committe being from the same floor ?

c. it is knows, that there are 3 families in the building with the same name, "smith". what is the probability of having two "smith"s in the committee ?

d. now let's assume we have 32 people ( 1 in each flat ), and still, 3 "smith"s. if we define a random variable of being a smith, what kind of variable is it and what's it's expectation ?

if you can help me with some of them, I'll really appreciate it !!

- July 22nd 2009, 01:57 PM #10

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- July 22nd 2009, 02:16 PM #11

- July 22nd 2009, 09:13 PM #12

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- July 23rd 2009, 02:16 PM #13

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