Chapter 15, Problem 5CT

To determine

To find: The whole number less then $500$ can formed.

Answer to Problem 5CT

The whole number less then $500$ can formed $68$ .

Explanation of Solution

Given information:

The given digit $1$ , $2$

  $3,4\text{and}5$ .

Calculation:

Calculate the expression is.

The $1$ -digit integers: consider a single box.

  $\begin{array}{l}U\\ \boxed{}\end{array}$

Enter the number in $4$ in the box.

  $\begin{array}{l}U\\ \boxed{4}\end{array}$

The $2$ -digit integers: consider a two box.

  $\begin{array}{l}TU\\ \boxed{}\boxed{}\end{array}$

Enter the number in $4$ in the box.

  $\begin{array}{l}TU\\ \boxed{}\boxed{4}\end{array}$

Enter the number in $2$ in the box.

  $\begin{array}{l}TU\\ \boxed{4}\boxed{4}\end{array}$

The $2$ -digit integers: consider a three box.

  $\begin{array}{l}HTU\\ \boxed{}\boxed{}\boxed{}\end{array}$

Enter the number in $4$ in the box

  $\begin{array}{l}HTU\\ \boxed{}\boxed{}\boxed{4}\\ HTU\\ \boxed{}\boxed{4}\boxed{4}\\ HTU\\ \boxed{3}\boxed{4}\boxed{4}\end{array}$

The number of integers

  $\begin{array}{l}=4+16+18\\ =68\end{array}$

Therefore the whole number less then $500$ can formed $68$ .