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Algebra

New kid on the Block

 Joined: 1 Jul 2009 Post: 3
1 Jul 2009 15:03:43 IST
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In how many ways can the letters of the word CINEMA be arranged so that the order of vowels do not c
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

In how many ways can the letters of the word CINEMA be arranged so that the order of vowels do not change?....Please Explain.

Blazing goIITian

Joined: 21 Mar 2009
Posts: 345
1 Jul 2009 22:58:07 IST
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by  order  of the  vowels , i assume that  the  relative  position of the  vowels  does not  change.(otherwise it becomes  a casebash , which  i am not interested in solving).

now  in CINEMA  if the  relative  positions  of  I,E,A  do not change , then the rmaining 3 letters  can be interchanged in 3!=6 ways.

if  u find that my assumption is wrong , then kindly explain the question more briefly.

Blazing goIITian

Joined: 21 Aug 2007
Posts: 384
1 Jul 2009 23:25:02 IST
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Hey mathie,even the position of the vowels matters,even if they are in the same order.

The answer will be 6c3X 6

(i.e the no of ways of choosing positions for the vowels X the no. of ways of aranging rest of the letters.)

Hot goIITian

Joined: 20 Jun 2008
Posts: 191
1 Jul 2009 23:33:13 IST
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by the order of vowels it means that only after the appearance of i ,the letter e should appear and only then should a appearin the word

Blazing goIITian

Joined: 8 Oct 2008
Posts: 8064
10 Jul 2009 17:42:30 IST
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dere are six places _ _ _ _ _ _ now we fix a order as such i ,e, a

dese can b filled in given order by selecting three places out of 6

wich can b done in 6c3 ways

nw in rest three places we can permutate remaining words in 3! ways

so total no. of ways 6c35!

here wat we hav done is first selected d place for vowels n then arranged remaining words

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