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Re: What is the probability that a 4 person committee chosen at random fro [#permalink]

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15 Jul 2015, 15:07

Can someone explain the reasoning behind 11C3 is it to choose the remaining members from the men and children. If so, why is that important if we just want to determine the probability of choosing exactly 1 woman from the group?

Can someone explain the reasoning behind 11C3 is it to choose the remaining members from the men and children. If so, why is that important if we just want to determine the probability of choosing exactly 1 woman from the group?

Yes, you are correct that the logic behind 11C3 is to choose 3 out of the remaining 11 'people'.

You need to know this number to calculate the number of ways you can select 'remaining' 3 people to make up the 4 member committee. When you just take the probability of selecting 1 women , you are still missing the probability of remaining 3 people. Total probability will be affected by both, probability of selecting 1 out of 7 women and probability of selecting 3 out of remaining 11 men+children.

What is the probability that a 4 person committee chosen at random fro [#permalink]

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28 Sep 2017, 13:30

Here is how I solved the problem:

Step 1) Write out all of the possibilities for the four slots (W= Women, NW= Not a Women). - W, NW, NW, NW - NW, W, NW, NW - NW, NW, W, NW - NW, NW, NW, W

There are 4 different arrangements.

Step 2) Calculate the probability of each arrangement separately combining them with "and" (meaning multiply). And remember that with each selection, the amount available becomes one smaller.

Chance of W, NW, NW, NW = (7/18)(11/17)(10/16)(9/15) Chance of NW, W, NW, NW = (11/18)(7/17)(10/16)(9/15) Now stop.. Realize that no matter the arrangement, the numerators and denominators will remain the same.

Step 3) Simplify and calculate 4*[(7/18)(11/17)(10/16)(9/15)] = 77/204

*With practice you should be able to quickly determine that there are four ways of arrangement and that they will all yield the same results, which puts you straight to step 3!

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