Chapter 13.1, Problem 25AYU

Four-digit Numbers How many four-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? Repeated digits are allowed.

To determine

To find: How many 4 digit numbers can be formed using the given digits, if repeated digits are allowed and first digit cannot be 0.

Answer to Problem 25AYU

9000

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, number of choices for the first digit is 9 (since 0 cannot be the first digit).

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.

Hence, there are $9*10*10*10=9000$ different ways, the selection can be done.