Probability help please!

Question

Assume that product codes are formed from the letters R, Q, and T, and consist of 6 not necessarily distinct letters arranged one after the other. For example, RRRRRT is a product code.



(1) How many different product codes are there? 

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

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

Answer 1

Giselle

(1) well for each letter there are 3 possibilities R,Q,T. So total possible codes = 3 x 3 x 3 x 3 x 3 x 3

(2) if you exclude T, 2 possibilities for each letter, SO 2 x 2 x 2 x 2 x 2 x 2

(3) If there is one Q. There are 6 ways of choosing the place where the Q is.

Then having decided that, there are 5 places to fill with 2 possible letters.

So we can fill those 5 places in 2 x 2 x 2 x 2 x 2 ways

So total ways = 6 x 2 x 2 x 2 x 2 x 2

Mike