SOLUTION: A committee of six Congressmen will be selected from a group of four Democrats and seven Republicans. Find the number of ways of obtaining exactly one democrat.

Question 1162995: A committee of six Congressmen will be selected from a group of four Democrats and seven Republicans. Find the number of ways of obtaining exactly one democrat.
Answer by ikleyn(52887) (Show Source): You can put this solution on YOUR website!
.


One democrat can be selected by 4 ways (obviously);


the remaining 5 republicans can be selected by   =  = 21 ways.


These selections in separate groups are INDEPENDENT --- therefore, the final answer is the product  4*21 = 84.

Solved.

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On Combinations, see the lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - Problems on Combinations with restrictions
    - Fundamental counting principle problems
    - Math circle level problem 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

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