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How many different words can be formed from with the letters of the word “RAINBOW” so that the vowels occupy odd places. 

(a) 676 

(b) 336 

(c) 576 

(d) 144

1 Answer

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Best answer

(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.

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