SOLUTION: A committee of 5 people is selected from a group of 7 men and 8 women. In how many ways can the committee be selected so it contains at least 1 woman?

Question 1149503: A committee of 5 people is selected from a group of 7 men and 8 women. In how many ways can the committee be selected so it contains at least 1 woman?

Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.


In all, there are 7+8 = 15 individuals,


and 5 people of 15 can can be selected in   ways.


It is the total possible number of groups of 5 individuals.


Now, the committee of 5 people, consisting of men ONLY, can be selected in   ways.


The answer to the problem question is the COMPLEMENT of    to  , i.e. the difference   - .


You do the calculations, following my instructions.

Answered.

Shortly speaking, from the number of all possible groups of 5 I subtracted the number of such groups consisting of men only.

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On Combinations, see introductory 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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