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Question

In how many ways can the letters of the word COMBINE be arranged so as to begin and end with a vowel? Also find the number of words that can be formed without changing the relative order of the vowels and consonants.

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Solution

Total =7 out of which 3 vowels 4 consonants
(i) 3P2×5!=6×120=720
(ii) The three vowels shall continue to occupy the 2nd,5th and 7th position only. In other words, these three vowels can be arranged in these three places in 3!=6 ways. Similarly the four consonants can be arranged in 4!=24 ways. Thus the total number of letters is 6×24=144 in which the relative order is maintained.

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