Find the number of permutations of the word OMEGA in which
(i) Vowels occupying odd places
(ii) The first letter is a vowel.

Explanation

To solve the problem, we need to find the number of permutations of the word "OMEGA" under two different conditions. The word "OMEGA" consists of 5 letters: O, M, E, G, A, where O, E, and A are vowels, and M and G are consonants.

### Part (i): Vowels occupying odd places

1. **Identify the positions**: The word has 5 positions: 1, 2, 3, 4, 5. The odd positions are 1, 3, and 5.

2. **Place vowels in odd positions**: We have 3 vowels (O, E, A) that need to occupy the 3 odd positions (1, 3, and 5). The number of ways to arrange 3 vowels in 3 positions is given by the factorial of the number of vowels:
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