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letters of the word MACHINE

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by vikram4689 » Tue Apr 10, 2012 7:50 am
Find the no of ways in which the letters of the word MACHINE can be arranged so that the vowels may occupy only odd positions.

a) 3!*4! b) 7P3 * 4! c) 7P4*3! d) none e) 4!*4!

[spoiler]IMO E, Vowels at 3 odd places can be arranged in 4P3(4!) ways and 4 consonants can be arranged in 4! ways so 4!*4!
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by bryan88 » Tue Apr 10, 2012 9:50 am
Total letters 7
vowels 3; odd positions 4
Cons 4; Even positions 3

- - - - - - -
1 2 3 4 5 6 7

For consonants- 4 consonants in 3 place. 4P3=4!
For vowels-Place at(135,137,157 or 357) 4*3!=4!

Ans-Combining- 4!*4!
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by shubham_k » Tue Apr 10, 2012 10:30 am
Out of 4 odd positions we have 3 vowels, so it can be done in 4P3 ways = 4!. Out of the remaining 4 positions first can be filled in 4 ways second in three ways and the third in 2 ways and last one is taken care on its own so they can be together arranged in 4*3*2*1 = 4! ways. So total ways of forming the word is 4!*4!.
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by shubham_k » Tue Apr 10, 2012 10:30 am
Out of 4 odd positions we have 3 vowels, so it can be done in 4P3 ways = 4!. Out of the remaining 4 positions first can be filled in 4 ways second in three ways and the third in 2 ways and last one is taken care on its own so they can be together arranged in 4*3*2*1 = 4! ways. So total ways of forming the word is 4!*4!.

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