Multiple choice

How many 4-letter words (with or without meaning) containing two vowels can be constructed using only the letters (without repetition) of the word 'LUCKNOW'?

  1. 240

  2. 200

  3. 150

  4. 120

  5. N.A
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A Correct answer
Explanation

LUCKNOW has 7 letters: L, U, C, K, N, O, W. Vowels are U, O (2). Consonants are L, C, K, N, W (5). To pick 4 letters with 2 vowels: Choose 2 vowels (2C2 = 1) and 2 consonants (5C2 = 10). Total sets = 10. Each set has 4! = 24 arrangements. 10 * 24 = 240.

AI explanation

The word LUCKNOW contains 2 vowels (U, O) and 5 consonants, and we must select 2 vowels and 2 consonants. The number of ways to choose the letters is 2C2 x 5C2 = 1 x 10 = 10 ways. Since the 4-letter word must have distinct arrangements without repetition, we multiply this by 4 factorial, so 10 x 24 = 240.

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