Can you find the 7 lettered "Good Words"
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?
Note: This sum is from ISI entrance exam.
The answer is 192.
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1 solution
Let x n be the total number of favourable strings of length n. Now, irrespective of the letter that comes in the second last position (from right), there are always 2 choices to fill the the last position. Hence x n = 2 x n − 1 . And we know that x 1 = 3 . Solving this recurrence equation we get x n = 3 × 2 n − 1 . Hence, substituting n=7 we get x 7 = 1 9 2 .