How many three-letter code symbols can be formed using a set of 5 different letters if repetition is not allowed? To solve this I would only need to multiply 5x4x3 right? how would I solve it if repetition was allowed?

it would be 5x5x5

Could you please clarify? 5x5x5 would be used if repetition WAS allowed and 5x4x3 would be used if repetition is NOT allowed.... right?

I answered you last question.

rep. allowed: 5x5x5
rep. not allowed : 5x4x3

To find the number of three-letter code symbols that can be formed using a set of 5 different letters without repetition, you are correct in using the multiplication principle.

To explain, think of the problem as a series of choices. For the first letter, you have 5 options. Once you've made the first choice, you have 4 remaining letters to choose from for the second letter. Finally, for the third letter, you have 3 options. By multiplying these choices together (5 * 4 * 3), you find that there are 60 different three-letter code symbols that can be formed without repetition.

Now, if repetition of letters is allowed, the process is slightly different. In this case, you can choose any one of the 5 letters for each of the three letter positions independently. So for each position, you have 5 options. Since these positions are independent, you multiply the number of options for each position together once again.

So, to find the number of three-letter code symbols with repetition allowed, you would calculate it as 5 * 5 * 5, which equals 125. Therefore, there are 125 different three-letter code symbols that can be formed when repetition is allowed.