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How many distinct rearrangements of the letters in "sleepless" are there?

User GgnDpSingh
by
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1 Answer

5 votes

Answer:


N = 5040

Explanation:

Required

Arrange the letters of "sleepless"

First, we count the number (n) of characters


n = 9

First, we count the number (n) of repeated characters


s = 3


e = 3


l = 2

The arrangement (N) is then calculated as follows;


N = (n!)/(s!e!l!)

This gives:


N = (9!)/(3!3!2!)


N = (9*8*7*6*5*4*3*2*1)/(3*2*1*3*2*1*2*1)


N = (362880)/(72)


N = 5040

Hence, there are 5040 distinct arrangements

User IPherian
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