SOLUTION: How many 26-letter arrangemenst of the alphabet have no two vowels together?

Algebra ->  Probability-and-statistics -> SOLUTION: How many 26-letter arrangemenst of the alphabet have no two vowels together?      Log On


   

Question 32283: How many 26-letter arrangemenst of the alphabet have no two vowels together?
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
PLACE 21 CONSONANTS FIRST..THESE CAN BE ARRANGED IN
21P21 WAYS=21!WAYS
THEY HAVE 20 INTERSPACES AND 2 OUTER SPACES,WHERE WE CAN KEEP THE OWELS SO THAT THEY NEVER COME TOGETHER AND ALWAYS SEPERATED BY A CONSONANT.
IN 22 SPACES , 5 VOWELS CAN BE ARRANGED IN 22P5 WAYS=22!/(22-5)!=21!/17!
SO TOTAL NUMBER OF ARRANGEMENTS = 21!*22!/17!