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Chapter 13: Q. 31 (page 855)

Forming Codes How many two-letter codes can be formed using the letter A, B, C, and D? Repeated letters are allowed.

Short Answer

Expert verified

There are 16 ways to write a two-letter code.

Step by step solution

01

Step 1. Given information.

Two-letter code is to be formed using the letter A, B, C, and D.

Repeated letters are allowed.

02

Step 2. Determine the possible number of codes.

We are choosing 2 letters from 4 letters and arranging them in order. In the ordered arrangement a letter may be repeated.

This is an example of a permutation with repetition in which 2 objects are chosen from 4 distinct objects.

Each selection has 4 choices. By the Multiplication Principle, we get

4·4=16

03

Step 3. Conclusion.

There are 16 ways to write a two-letter code.

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