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Chapter 13: Q. 33 (page 855)

Forming Numbers How many three-digit numbers can be formed using the digits 0 and 1? Repeated digits are allowed.

Short Answer

Expert verified

There are 4 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 and 1.

Repeated digits are allowed.

02

Step 2. Determine the possible three-digit numbers.

This is an example of a permutation with repetition.

  • Selection of the first digit has only 1 choice because zero cannot be in the first place.
  • The selection of the second digit has 2 choices (0 or 1).
  • The selection of the third digit has 2 choices (0 or 1).

By the Multiplication Principle, we get

1路2路2=4

03

Step 3. Conclusion.

There are 4 ways to write a three-digit number.

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