Chapter 13, Problem 9CT

To determine

To find: How many distinct 8-letter words can be form the letters in the word $REDEEMED$ .

Answer to Problem 9CT

The distinct 8 letter words are $840.$

Explanation of Solution

Given: $REDEEMED$

Concept used: $\frac{n!}{n_1!n_2!--n_k!}$

Here $REDEEMED$ is given.

It has to find distinct 8 letters words.

The number of permutation of $n$ objects of which $n_1$ are one kind, $n_2$ are of a second kind,……, and $n_k$ are of a $kth$ kind, where

  $n=n_1+n_2+-----+n_k$ is

  $\frac{n!}{n_1!n_2!--n_k!}$

“R” appears 1 times,

“E” appears 4 times,

“D” appears 2 times,

“M” appears 1 times,

  $\begin{array}{l}1+4+2+1=8\\ \frac{8!}{1!4!1!2!}\\ =\frac{4!\mathrm{.5.6.7.8}}{4!2.1}\\ =\frac{\mathrm{5.6.7.8}}{2.1}\\ =840\end{array}$

Hence, the distinct 8 letters words are $840.$