Question

CH 06 SEC 1 EX 08 Main (Dependent Multi-part Problem - Assign all parts) - Counting Principles. Note: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider people with three-letter initials. CH 06 SEC 1 EX 08 (b) - Counting Principles. How many different three-letter initials are there with no letters repeated?

a) 26
b) 78
c) 156
d) Numeric response

Answer 1

There are 15,600 different three-letter initials with no letters repeated.

Step-by-step explanation:

To find the number of different three-letter initials with no letters repeated, we need to consider the number of choices for the first initial, the number of choices for the second initial, and the number of choices for the third initial.

For the first initial, we have 26 choices (one for each letter of the alphabet). For the second initial, we have 25 choices (since we cannot choose the first initial again). And for the third initial, we have 24 choices (since we cannot choose any of the letters that have already been chosen).

Using the counting principle, we multiply the number of choices for each initial together: 26 * 25 * 24 = 15,600.

Therefore, there are 15,600 different three-letter initials with no letters repeated.