Multiple choice

The numbers of words formed letters of the word $'EAMCET'$ so that no two vowels come together, is-

  1. $360$
  2. $144$
  3. $72$
  4. $54$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

EAMCET has 6 letters: E, A, M, C, E, T. Vowels are E, A, E. Consonants are M, C, T. Arrange consonants first: 3! = 6 ways. There are 4 gaps between consonants: _ M _ C _ T _. Choose 3 gaps for vowels: 4C3 = 4. Arrange vowels: 3!/2! = 3. Total = 6 * 4 * 3 = 72.

AI explanation

The word EAMCET has 6 letters with 3 vowels (E, A, E) and 3 consonants (M, C, T). The consonants can be arranged in 3! = 6 ways, creating 4 gaps for the vowels. Choosing 3 of these 4 gaps and arranging the 3 vowels gives 4C3 * (3! / 2!) = 4 * 3 = 12 ways. The total number of words is 6 * 12 = 72. The correct result is 72.

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