SOLUTION: In how many ways can a committee of 4 be selected from 8 and 6 men if Marge (One of the ladies) refuses to serve in the same committee as her ex-boyfriend, Joel (one of the 6 men).

Question 1126531: In how many ways can a committee of 4 be selected from 8 and 6 men if Marge (One of the ladies) refuses to serve in the same committee as her ex-boyfriend, Joel (one of the 6 men).
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
.

If neglect the restriction, then the number of ways is   =  =  = 1001.


Of this number of ways, some groups are prohibited. They are those that include Marge and Joel, complemented by 2 other, 
arbitrary chosen persons of remaining (8+6)-2 = 12 persons. 


So, the number of the prohibited groups is   =  = 66.


Then the answer to the problem's question is this difference


    1001 - 66 = 935.

Solved.

-------------------

On Combinations, see the lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - 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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