If the letters of the word PREVIOUS be arranged at random, what is the probability that all the vowels come together ?

• A. 1/10
• B. 1/12
• C. 1/16
• D. 1/14

Answer: (D)

There are total eight letters ∴ n(S) = 8PB = 8!As all vowels should come together we assume them as one letter. Here E, I, O and U together are taken as one, so the number of letter is 4 + 1 = 5 and it can be arranged in 5P5 = 5! ways and the vowels can be arranged in 4! ways among themselves∴ n(E) = 4! x 5!∴ P(E) = 4!5! / 8!            = 4x3x2x5! / 8x7x6x5!            = 4x3x2 / 8x7x6            = 1/14