SOLUTION: In how many ways can you select a set of 3 letters from JasmineOrtz if the order of selection matters? In how many ways can you select a set of 3 letters if the order of selection

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Question 1159330: In how many ways can you select a set of 3 letters from JasmineOrtz
if the order of selection matters? In how many ways can you select a set of 3 letters if the order of selection does not matter? Thank you for your help I have been watching videos but I haven't been able to solve it

Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
In how many ways can you select a set of 3 letters from JasmineOrtz if the order of selection matters?
In how many ways can you select a set of 3 letters if the order of selection does not matter?
~~~~~~~~~~~~~~~~~~~

(a)  The word "JasmineOrtz" has 11 letters, and they all are different.


     So, when the order of selection does matter, you may 

         - put any of 11 letters in the first position, when you select; (it gives you 11 options)

         - put any other of remaining 10 letter in the second position ((it gives you 10 options)

         - put any other of remaining 9 letter in the second position ((it gives you 9 options)
.


    Therefore, you have 11*10*9 = 990 options (permutation) in all, in this case.



(b)  If the order does not matter, you should divide this number of 990 by 6,

     because any set of 3 letters has 3! = 1*2*3 = 6 permutations.

     
     So, the answer in this case is  990/6 = 165.

Solved.

---------------

To get elementary, basic knowledge on permutations, see these introductory lessons
    - Introduction to Permutations
    - PROOF of the formula on the number of Permutations
    - Simple and simplest problems on permutations
    - Special type permutations problems

    - 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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