Chapter 10, Problem 1T

Counting Three-digit Numbers If only the digits 0, 1, 2, 3, 4, 5, and 6 may be used, find the number of possibilities in each category.

three-digit numbers

To determine

To calculate: The number of possible 3-digit numbers if Digits to be used are 0,1,2,3,4,5,6.

Answer to Problem 1T

Solution:

The number of possible 3-digit numbers is 294.

Explanation of Solution

Given:

Digits to be used are 0,1,2,3,4,5,6.

Calculation:

As a total of 7 digits are provided to find the number of 3-digit numbers by using the provided digits.

So, out of these 7 digits, the number of digits that can be placed at unit’s place is 6, that is, $1,2,3,4,5,6$. Here, $0$ is excluded from the unit’s digit as the number will then be considered as 2-digit number for example: $023,045$.

And, all the 7 digits can be placed at tens and hundreds place.

So, number of 3-digit number possible are multiplication of number of digits available to place in unit’s place, number of digits available to tens place and number of digits available to hundreds place.

So, total number of way is;

$6\cdot 7\cdot 7=294$