Concept of “Permutation and Combination”–02

Question: In how many different ways can the letters of the word ORGANISE be arranged in such a way that all the vowels always come together and all the consonants always come together? [Ans. (b) 1152]  

(a) 576     (b) 1152   (c) 2880 (d) 1440   (e) None of these

Solution:

Detailed Explanation: The word “ORGANISE” contains 8 letters out of which 4 are vowels and 4 are consonant. If vowels and consonants are to come together always, then they can be treated as two different things which can be arranged by 2! Ways.

Again, 4 vowels can be arranged themselves by 4! ways and 4 consonants can also be arranged themselves by 4! ways.

Therefore, the total no. of ways = 2×4! ×4! = 1152 Ans.

 ORGANISE

 (OAIE) (RGNS)

       1           2

 2×4! ×4! = 1152 Ans.