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Chapter 13: Q. 32 (page 855)

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

Short Answer

Expert verified

There are 25 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, D, and E.

Repeated letters are allowed.

02

Step 2. Determine the possible number of codes.

We are choosing 2 letters from 5 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 5 distinct objects.

Each selection has 5 choices. By the Multiplication Principle, we get

5路5=25

03

Step 3. Conclusion.

There are 25 ways to write a two-letter code.

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