Question 1174360
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(1)   The formulation of the problem in your post is incorrect.


            You will not understand the solution, until you learn how to formulate the problem correctly.




(2)    For correct formulation and solution of similar  (TWIN)  problems see the link


<A HREF=https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1173142.html>https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1173142.html</A>


https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1173142.html




(3)  &nbsp;&nbsp;To learn the subject in more details, see my lesson

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Arranging-elements-of-sets-containing-undistinguishable-elements.lesson>Arranging elements of sets containing indistinguishable elements</A> 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;in this site.



Happy learning &nbsp;(!)



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<U>Comment from student</U>: &nbsp;&nbsp;Question 1174360 Do you mean the question is not well formulated?




<U>My response</U>.  &nbsp;&nbsp;Yes, &nbsp;exactly, &nbsp;the question &nbsp;IS &nbsp;NOT &nbsp;WELL &nbsp;FORMULATED.


The &nbsp;STANDARD &nbsp;formulation of this class of problems &nbsp;(and this concrete problem specifically) &nbsp;is &nbsp;THIS



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;How many &nbsp;DISTINGUISHABLE &nbsp;words can be formed using the letters of the word &nbsp;MISSISSIPPI ?



See and learn from the sources that I provided for you in my post above.




Thank you for asking.


It was VERY RIGHT STEP from your side to ask this question.




To understand these problems &nbsp;IN &nbsp;FULL, &nbsp;you need to learn two conceptions:


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;"distinguishable words"  &nbsp;&nbsp;and  &nbsp;&nbsp;"multiplicity of a letter in a word".


All explanations you will find in my sources, &nbsp;referred above.



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As my gift to you for asking your question, consider these lessons on PERMUTATIONS

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Permutations.lesson>Introduction to Permutations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-permutations.lesson>PROOF of the formula on the number of Permutations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Problems-on-Permutations.lesson>Simple and simplest problems on permutations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Special-type-permutations-problems.lesson>Special type permutations problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/How-many-different-permutations-may-exist-ubder-given-restrictions.lesson>Problems on Permutations with restrictions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Arranging-elements-of-sets-containing-undistinguishable-elements.lesson>Arranging elements of sets containing indistinguishable elements</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Persons-sitting-around-a-circular-table.lesson>Persons sitting around a cicular table</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Combinatoric-problems-for-entities-other-than-permutations-and-combinations.lesson>Combinatoric problems for entities other than permutations and combinations</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Fundamental-counting-principle-problems.lesson>Fundamental counting principle problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Nice-recreational-problems-on-permutations.lesson>Nice recreational problems on permutations</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/OVERVIEW-the-lessons-on-Permutations-and-Combinations.lesson>OVERVIEW of lessons on Permutations and Combinations</A>

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic &nbsp;"<U>Combinatorics: Combinations and permutations</U>". 



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.