0
$\begingroup$

A “good” word is any seven letter word consisting of letters from {A,B,C} (some letters may be absent and some letter can be present more than once), with the restriction that A cannot be followed by B, B cannot be followed by C, and C cannot be followed by A. How many good words are there?

This question has already been answered here: How many good words are there?

BUT i have doubts regarding the solution:

You can choose the first letter in 3 ways and any of the other letters in 2 ways, so there can be 3∗$2^6$=192 good words

The remaining six letters can be chosen in 6 ways each? But if we choose A at first place , then we can have A's following it , but once we put a 'C' in some position, it can't be followed by any more A's because "C cannot be followed by A"!

So, once we stumble upon a 'C' , we have only 1 possible letter for the remaining positions- which is "C".

I hope i made myself clear, any help will be highly appreciated.

$\endgroup$
1
$\begingroup$

The answer interprets followed by as meaning immediately followed by. It would allow ACBACBA as a good word because none of the restrictions are violated. I agree with that reading of the problem.

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ OH!!! Well, thank you so much. $\endgroup$ – MAthsjunky Mar 18 '17 at 14:53

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.