Multiple choice

The number of words that can be formed out of the letters of the word ARTICLE so that the vowels occupy even places is :

  1. 574

  2. 36

  3. 754

  4. 144
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

ARTICLE has 7 letters: A, R, T, I, C, L, E. Vowels are A, I, E (3). Consonants are R, T, C, L (4). Even positions are 2, 4, 6. We place the 3 vowels in these 3 positions in 3! = 6 ways. We place the 4 consonants in the remaining 4 positions in 4! = 24 ways. Total = 6 * 24 = 144.

AI explanation

The word ARTICLE has 7 letters, meaning there are 7 positions. The even positions are 2, 4, and 6, and the vowels are A, E, and I. The 3 vowels can be arranged in the 3 even places in 3P3, which is 3! = 6 ways. The remaining 4 consonants can be arranged in the 4 odd places in 4P4, which is 4! = 24 ways. The total number of words is 6 multiplied by 24, giving 144.

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