SOLUTION: How many subsets of {m,a,t,h,r,o,c,k,s} contain exactly 5 elements?

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Question 1116300: How many subsets of {m,a,t,h,r,o,c,k,s} contain exactly 5 elements?
Answer by ikleyn(52778) About Me  (Show Source):
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The original set has 9 elements.


The number of 5-element subsets is the number of combinations  C%5B9%5D%5E5 = %289%2A8%2A7%2A6%29%2F%281%2A2%2A3%2A4%29 = 126.


Each subset of 5 elements is a combination of 9 items taken 5 at a time. 


Each combination of 9 items taken 5 at a time is a subset of 5 elements.


Different subsets  <------> different combinations.

Solved and answered.

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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.