How many different product codes contain exactly one Y?

Question

Assume that product codes are formed from the letters X, Y, S, W, R, and U, and consist of 5 not necessarily distinct letters arranged one after the other. For example, XXRRY is a product code.

Answer 1

Since only one Y can be used, the remaining spots are restricted to the other 5 letters.  So we can set up our equation like so:

 

5×(5×5×5×5×1)=3125 labels can be made with only one Y

Answer 2

To count the product codes with exactly one Y, you select one of the 5 positions to be assigned Y. For each of the remaining 4 positions you can use any of the remaining 5 letters different from Y and only them. So, the number is

5x(5x5x5x5) = 5^5 = 3125 again.