Multiple choice

Find the number of permutations that can be made from the letters of the word OMEGA, if the vowels occupy odd places.

  1. 12 ways

  2. 6 ways

  3. 16 ways

  4. 20 ways
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A Correct answer
Explanation

OMEGA has 5 letters: 3 consonants (M, G, N? No, O, M, E, G, A). Vowels are O, E, A. Consonants are M, G. Odd places are 1, 3, 5. There are 3 odd places and 3 vowels. The number of ways to arrange the vowels in odd places is 3! = 6. The remaining 2 consonants can be arranged in the 2 even places in 2! = 2 ways. Total = 6 * 2 = 12.

AI explanation

The word OMEGA has 5 positions, with 3 odd places (1st, 3rd, and 5th) and 3 vowels (O, E, A). We first arrange the 3 vowels in the 3 odd places in 3! = 6 ways, and then arrange the 2 remaining consonants in the 2 even places in 2! = 2 ways. Multiplying these independent arrangements gives 6 x 2 = 12 ways.

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