SOLUTION: a club consisting of six distinct men and seven distinct women; a.) how many ways can we select a committee of five persons?; b.) In how many ways can we select a committee

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Question 1183045: a club consisting of six distinct men and seven distinct women;
a.) how many ways can we select a committee of five persons?;
b.) In how many ways can we select a committee of three men and four women?
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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a club consisting of six distinct men and seven distinct women;
a.) how many ways can we select a committee of five persons?;
b.) In how many ways can we select a committee of three men and four women?
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Start noticing that there are 6 + 7 = 13 persons, in total. 


(a)  In  C%5B6%2B7%5D%5E5 = C%5B13%5D%5E5 = %2813%2A12%2A11%2A10%2A9%29%2F%281%2A2%2A3%2A4%2A5%29 = 1287  ways.



(b)  In  C%5B6%5D%5E3%2AC%5B7%5D%5E4 = %28%286%2A5%2A4%29%2F%281%2A2%2A3%29%29%2A%28%287%2A6%2A5%29%2F%281%2A2%2A3%29%29 = 20*35 = 700 ways.

Solved.

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This problem is on COMBINATIONS.


On Combinations,  see introductory lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - Fundamental counting principle problems
    - OVERVIEW of lessons on Permutations and Combinations
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic  "Combinatorics: Combinations and permutations".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.


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A note to the composer of the problem


            When you formulate the problem,  do not use the word  "distinct"  when you say

                    "six distinct men and seven distinct women".

            It is clear even without your words that they all are distinct - they  CAN  NOT  be identical.


Unnecessary words do not make your text stronger ---- in opposite, they make your text weaker.