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Permutation under Restriction

All the lette...

Question

All the letters of the word EAMCET are arranged in all possible ways. The number of such arrangements in which no two vowels are adjacent to each other is

A

360

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B

144

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C

72

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D

54

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Solution

The correct option is B $72$
Gap method, Consonants M, C, T in 3! = 6 ways and 4 gaps and 3 vowels (2 alike) in $^{4} P_{3} \frac{1}{2!} = 12$ ways.
$12 \times 6 = 72.$

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