The number of words which can be made out of the letters of the word 'MOBILE' when consonants occupy odd…

The number of words which can be made out of the letters of the word 'MOBILE' when consonants occupy odd places is
  1. $20$
  2. $36$
  3. $30$
  4. $720$

Solution

There are 3 vowels and 3 consonants
$\therefore$ Number of ways to fill and arrange odd places with consonants $={ }^3 C_3 \cdot 3$ ! and number of ways to fill remaining 3 places $=3$ ! $\therefore$ The number of words $={ }^3 C_3 \cdot 3 ! \cdot 3 !=36$

Asked in: AP EAMCET 2021 (23 Aug Shift 2)

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