Chapter 6, Problem 5CST

To determine

To calculate: the different possible codes for assigns item.

Answer to Problem 5CST

The different possible codes for assigns item is $15600$ .

Explanation of Solution

Given information : the using capital letters provided in the question,

  $3$ .

Formula used:

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

Calculation : to find the different possible codes for assign each item,

There are total $26$ capital letters, an to make code choose $3$ capital letters,

So take $3$ capital letters from total capital letters,

  $\begin{array}{l}P{}_r=\frac{n!}{\left(n-r\right)!}\\ P{}_3=\frac{26!}{\left(26-3\right)!}\text{ [substitute n by 26 and r by 3]}\\ P{}_3=\frac{26·25·24·23!}{\left(23\right)!}\text{ [subtract, expand factorial and divide out common factors]}\\ P{}_3=26·25·24\text{ [simplify]}\\ P{}_3=15600\text{ [multiply]}\end{array}$

Hence, The different possible codes for assigns item is $15600$ .