Chapter 8.5, Problem 17E

(a)

To determine

To find: the number of three digit numbers can be formed under given condition.

Answer to Problem 17E

The number of three digit numbers can be formed under given condition is 900.

Explanation of Solution

Given information:

Given condition

The leading digit cannot be 0.

Calculation:

Consider the three digit number. If the leading digit cannot be zero then possible numbers are:

  $\begin{array}{l}=9\times 10\times 10\\ =900\end{array}$

(b)

To determine

To find: the number of three digit numbers can be formed under given condition.

Answer to Problem 17E

The number of three digit numbers can be formed under given condition is 648

Explanation of Solution

Given information:

The leading digit cannot be 0 and no repetition of digits is allowed.

Calculation:

If the leading digit cannot be zero and repetition is not allowed then possible numbers are:

  $\begin{array}{l}=9\times 9\times 8\\ =648\end{array}$

(c)

To determine

To find: the number of three digit numbers can be formed under given condition.

Answer to Problem 17E

The number of three digit numbers can be formed under given condition180.

Explanation of Solution

Given information:

The leading digit cannot be 0 and the number must be a multiple of 5.

Calculation:

If the leading digit cannot be zero and the number must be a multiple of 5 then possible numbers are:

  $\begin{array}{l}=9\times 10\times 2\\ =180\end{array}$