Chapter 11.3, Problem 50PPSE

Solution

To identify:How many five-letter permutation can you form from the letter of the word COMPUTER

The number of five letter permutation of the letter of the word COMPUTER is $P{}_5=6720$

Given information:

The given word is COMPUTER

Explanation:

Consider the information.

Since in words order of letters matters, so use permutation formula

So number of five letter permutations of the letters of the word COMPUTER is $P{}_5$

Since,

  $P{}_r=\frac{n!}{\left(n-r\right)!}$

And

  $n!=n\cdot \left(n-1\right)\cdot \left(n-2\right)\mathrm{......3}\cdot 2\cdot 1$

So $P{}_5$ is evaluated as

  $\begin{array}{l}P{}_r=\frac{n!}{\left(n-r\right)!}\\ n!=n\cdot \left(n-1\right)\cdot \left(n-2\right)\mathrm{......3}\cdot 2\cdot 1\\ P{}_5=\frac{8!}{\left(8-5\right)!}\\ P{}_5=\frac{8!}{3!}\\ P{}_5=\frac{8\cdot 7\cdot 6\cdot 5\cdot \left(3!\right)}{3!}\\ P{}_5=6720\end{array}$

Hence the number of five letter permutation of the letter of the word COMPUTER is $P{}_5=6720$