If we permute 5 letters of the word ‘lemon’ in 5!ways.In how many words vowels do not come together? A.120 B.72 C.48 D.24
Answers
Answer:
There are 72 words in which vowels do not come together. Step-by-step explanation: There are two vowels in the word lemon.
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Given,
Number of words = 5
Word = lemon
To Find,
Total ways in which vowels do not come together =?
Solution,
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 * 2
Total 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 =
⇒ Total ways - Total ways to arrange letters with vowels come together
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.