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Chapter 13: Q. 34 (page 855)

Forming Numbers How many three-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9? Repeated digits are allowed.

Short Answer

Expert verified

There are 900 ways to write a three-digit number.

Step by step solution

01

Step 1. Given information.

A three-digit number is to be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Repeated digits are allowed.

02

Step 2. Determine the possible three-digit numbers.

This is an example of a permutation with repetition and the total number of digits is 10.

  • Selection of the first digit has 9 choices because zero cannot be in the first place.
  • The selection of the second digit has 10 choices.
  • The selection of the third digit has 10 choices.

By the Multiplication Principle, we get

9路10路10=900

03

Step 3. Conclusion.

There are 900 ways to write a three-digit number.

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