How many permutations of the multiset $S = \{3\cdot a, 3\cdot b, 3\cdot c\}$ no two identical consecutive letters appear?

Asked Jul 08 '20 at 01:38

Active Jul 08 '20 at 03:07

Viewed 54 times

I have to find the number of permutations of $S = \{3\cdot a, 3\cdot b, 3\cdot c\}$ in which two equal consecutive letters do not appear.

I'm trying to do it for inclusion-exclusion principle, but I can't reach the correct answer.

According to the text, the answer should be 174 permutations.

edited Jul 08 '20 at 03:07

RobPratt

asked Jul 08 '20 at 01:38

The textbook answer appears correct (direct counting verification). I'd do recursion with f(first_letter, number of 'a's left to place, number of 'b's left to place, number of 'c's left to place) but it appears rather lengthy. If you don't mind showing all your work, it would be easier to find a mistake, if there is one. Thanks. – Alexey Burdin Jul 08 '20 at 01:50

0 Answers0