SOLUTION: In how many ways can letters be chosen from {J,K,L,M,N,O,P,Q,R,S} assuming that the order of the choices doesn't matter and that repeats are not allowed?

Question 1143699: In how many ways can letters be chosen from {J,K,L,M,N,O,P,Q,R,S} assuming that the order of the choices doesn't matter and that repeats are not allowed?
Answer by ikleyn(52915) (Show Source): You can put this solution on YOUR website!
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There are 10 letters in the set, in all, and they all are distinct.


You can select first letter by 10 ways.

Then you can select the second letter by 9 ways among the 9 remaining letters.

Then you can select the second letter by 8 ways among the 8 remaining letters.


    . . .        and   so   on   . . . 


Then you can select the 9-th letter by 2 ways among the 2 remaining letters.

Then you can select the last, 10-th letter by only 1 way among the 1 remaining letter 
    (practically, you just have no selection choice at this step).



In all, there are 10! = 10*9*8*7* . . . *2*1 = 7257600 ways/selections.    ANSWER

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This problem is about PERMUTATIONS.

On permutations, see the introductory lessons
    - Introduction to Permutations
    - PROOF of the formula on the number of Permutations
    - Problems on Permutations

    - 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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