Question

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

Answer 1

Answer:

$N = 5040$

Step-by-step 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;

$N = \frac{n!}{s!e!l!}$

This gives:

$N = \frac{9!}{3!3!2!}$

$N = \frac{9*8*7*6*5*4*3*2*1}{3*2*1*3*2*1*2*1}$

$N = \frac{362880}{72}$

$N = 5040$

Hence, there are 5040 distinct arrangements