(c) 576
There are 7 letters in the word RAINBOW out of which 4 are consonants and 3 are vowels.
1 2 3 4 5 6 7
In order that the vowels may occupy odd places, we first of all arrange any 3 consonants in even places in 4P3 ways and then the odd places can be filled by 3 vowels and the remaining 1 consonant in 4P4 ways. So,
Required number of words = 4P3 × 4P4 = 24 × 24 = 576.