Chapter 11.6, Problem 37E

Solution

a.

To calculate: tofind the3-digit number can make by using digit $1,2,3$ exactly once.

The numbers of 3-digit when using each number once is $6$ .

Given : consider, the information provided in the question,

Given digits = $1,2,3$

Calculation :

When we use the numbers only once then because we use the number exactly once so number of 3-digit ,

  $3!=3·2·1$

  $3!=6$

Thus,The numbers of 3-digit when using each number once is $6$ .

b.

To calculate: to find the 3-digit number can make by using digit $1,2,3$ more than once.

The numbers of 3-digit when using each number more than once is $27$ .

Given : consider, the information provided in the question,

Given digits = $1,2,3$

Calculation :

When we use the number more than one time so there is same possibility to gave the number on every digit place,

  $3·3·3=27$

Thus, The numbers of 3-digit when using each number more than once is $27$ .