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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 |
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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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