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(52878)   (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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