Question 1198366
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How many different 4-letter permutations can be formed from the letters in the word REPRESENT?
I know that if I want deffrent letter it would be permutation
like 6P4 = 360
but how about the repeated letters like the E 3 times and r 2 times?
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<pre>
Since they want you use different letters with no repetition,
you should first determine the number of different letters in the word REPRESENT.


It is easy to do: the number of different letters is  R + E + P + S + N + T = 6.


Now you apply the method which you know, and you get this answer:


    the number of different 4-letter permutations is  6*5*4*3 = 360

    (four consecutive integer factors in descending order, starting from the number of 6).
</pre>

Solved, with complete explanations.



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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Another interpretation is possible considering/allowing repeating letters.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;@ewatrr tried to implement it, but her calculations are erroneous.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;See my calculations for this case below.



<pre>
There are 6 different letters; of them, letter "E" has multiplicity 3
and letter "R" has multiplicity 2.


We have 360 permutations without repetition, as I counted above.


Next, with 3 "E" and one single letter from remaining 5 letters {R,P,S,N,T} we have 5*4 = 20 additional permutations.


Next, with 2 "E" and 2 "R", we have  {{{4!/(2!*2!)}}} = {{{24/4}}} = 6 additional distinguishable permutations.


Next, with 2 "E" and 2 other single letters from the remaining 6-1 = 5 other unique letters {R,P,S,N,T}, 
we have {{{5*4*C[4]^2}}} = 20*6 = 120 additional distinguishable permutations.


Next, with 2 "R" and 2 other single letters from the remaining 6-1 = 5 other unique letters {E,P,S,N,T}, 
we have {{{5*4*C[4]^2}}} = 20*6 = 120 additional distinguishable permutations.


In all, there are  360 + 20 + 6 + 120 + 120 = 626 permutations of this kind.    <U>ANSWER</U>
</pre>

So, you have solutions for both possible interpretations.