Finite Product Codes

Question

Assume that product codes are formed from the letters T, Z, X, W, R, Q, and Y, and consist of 3 not necessarily distinct letters arranged one after the other. For example, TTW is a product code.

How many different product codes contain exactly one T?

Answer 1

Sabian

Well suppose there were 5 letters : T, Z, X, W, R.

If the code contains exactly one T , there are 3 cases

1. 1st letter only is T, the others can be anything else. 2nd letter - 4 possibilities, 3rd letter , 4 so total possible ways 4 x 4 = 16
2. 2nd and 3rd letter T. 16 possibilities for each (same argument as 1)
3. So total possible codes : 16 + 16 + 16 = 48

Now extend this method to your situation

1.