Question 1142237
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<pre>
The number of distinguishable arrangements is  {{{10!/(2!*2!)}}} = 907200.


Here 10 is the number of letters in the given word;  2! is to account for 2 identical letters "o"


and the other 2! is to account for 2 identical letters "p".



    The "magic" word is "population", I think.



The probability to get this arrangement among all other distinguishable arrangements is  {{{1/907200}}}.


The probability to have the relevant permutation among all possible permutations is the same value  {{{1/907200}}}.
</pre>


Regarding the other problem, there is a rule in this forum, that each post can carry <U>ONE and ONLY ONE PROBLEM</U>.



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To see other solved problems on distinguishable arrangements/permutations, look into the lesson

&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> 

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 lesson is 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.