Chapter 13.1, Problem 26AYU

Five-digit Numbers How many five-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if the first digit cannot be 0 or 1? Repeated digits are allowed.

To determine

To find: How many 5 digit numbers can be formed using the given digits, if repeated digits are allowed and first digit cannot be 0 or 1.

Answer to Problem 26AYU

80000

Explanation of Solution

Given:

The digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Formula used:

If a task consists of a sequence of choices in which there are $p$ selections for the first choice, $q$ selections for the second choice, $r$ selections for the third choice, and so on, the task of making these selections can be done in $pqr$ ... different ways.

Calculation:

In this task, since 0 or 1 cannot be first digit.

Number of choices for the first digit is 8.

Number of choices for the $2^{nd}$ digit is 10.

Number of choice for the $3^{rd}$ digit is 10.

Number of choice for the $4^{th}$ digit is 10.

Number of choice for the $5^{th}$ digit is 10.

Hence, there are $8*10*10*10*10=80000$ different ways, the selection can be done.