If we permute 5 letters of the word ‘lemon’ in 5! Ways. In how many words vowels do not come together?
A) 170
B) 72
C) 48
D) 24
Answer & Solution
Answer: Option BSolution:
Total letter if vowels come together = 4 [l , m , n , (e,o)]
Ways to arrange 4 vowels = 4!
Ways to arrange 2 vowels = 2!
Total ways to arrange letters with vowels come together = 4! *2!
Total ways to arrange letters with vowels come together = 24 * 2Total ways to arrange letters with vowels come together = 48
Total ways to arrange 5 letters = 5! = 120 ways
Total ways of arranging vowels so that vowels do not come together
⇒ 120 - 48 = 72 ways.
Hence, in 72 words vowels do not come together.