Egeg G.

asked • 04/14/22

there 10 and 4 women applying to be members of a 3 person committee Is this a permutation or combination? Justify your answer.

there are 10 and 4 women applying to be members of a 3-person committee Is this a permutation or combination? Justify your answer.

Mark M.

What is the difference between a permutation and a combination?
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04/14/22

Paul M.

tutor
The answer depends upon question. For example, "How many arrangements of committee members are possible?" versus "How different committees are possible?"
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04/14/22

Peter R.

tutor
If order doesn't matter or if the men vs. women assignments are not important, then it's a combination.
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04/14/22

Mark M.

Would expect a tutor to know the difference. The student knowing the difference is of importance.
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04/14/22

Vahan P.

tutor
Did you mean to write 10 men and 4 women? And how many men and women are in the committee? If you are choosing a set from a larger set, you are using a combination. You would use a permutation if the order of those in the committee was important.
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04/15/22

Jeremy L.

tutor
It is a combination. If your computation involves a situation where the order matters, then it is a permutation.
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04/16/22

Frank T.

tutor
10 what and 4 women?
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04/16/22

1 Expert Answer

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Robert K. answered • 04/16/22

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It's a simple combination.


How many ways can we pick 3 people from a group of 14?


We are not trying to put them in specific jobs on the committee. Nor are we saying how many of the 3 people must be either men or women.


So depending on what notation you are using it will be 14C3 or C(14,3). The value can be obtained using the key on the calculator or by doing it youself as follows.


14C3 = (14x13x12)/(1x2x3) = 364


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