1. ## number of codes

hey i would really appreciate it if somebody could answer this:

Assume that product codes are formed from the letters S, W, Q, T, R, and Y, and consist of 4 not necessarily distinct letters arranged one after the other. For example, SSWR is a product code.

(1) How many different product codes are there?

i got this one, it's 6^4 because there are 4 stages and each has 6 options.

(2) How many different product codes do not contain W?

i got this one too, it's 5^4 because instead of 4 stages with 6 options, there are 4 stages with 5 options.

(3) How many different product codes contain exactly one R?

this is the one i haven't been able to get. help please?

2. The answer is 4 x 5^3

This is because you have exactly one "R", so you first put an "R" in the product code, and then count the number of places it can be (it can be in four places). Then you have 3 decisions with 5 options for the remaining 3 spots, so you multiply by 5^3.

3. thanks. that helps a lot.