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Question

Question: The number of words which can be made out of the letters of the word ‘MOBILE’ when consonants always...

The number of words which can be made out of the letters of the word ‘MOBILE’ when consonants always occupy odd places is

A

20

B

36

C

30

D

720

Answer

36

Explanation

Solution

The word ‘MOBILE’ has three even places and three odd places. It has 3 consonants and 3 vowels. In three odd places we have to fix up 3 consonants which can be done in 3P33 ⥂ P_{3} ways. Now remaining three places we have to fix up remaining three places which can be done in 3P33P_{3} ways.

The total number of ways = 3P3×3P3=363P_{3} \times^{3}P_{3} = 36.