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# In how many ways can the letters of the word "COMPUTER" be arranged?

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Manager
Status: exam is close ... dont know if i ll hit that number
Joined: 06 Jun 2011
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Location: India
Concentration: International Business, Marketing
GMAT Date: 10-09-2012
GPA: 3.2
In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink]

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10 Jan 2012, 07:08
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In how many ways can the letters of the word "COMPUTER" be arranged?

1}Vowels occupy the even positions.
i mean what are the possibile arrangements???
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Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink]

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12 Jan 2012, 06:27
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mohan514 wrote:
On how many ways can the letters of the word "COMPUTER" be arranged?

1}Vowels occupy the even positions.
i mean what are the possibile arrangements???

I think it's meant that vowels can occupy only even positions:

C|O|M|P|U|T|E|R
O|E|O|E|O|E|O|E (O and E stand for odd and even positions respectively).

# of arrangements would be $$C^3_4*3!*5!=4!*5!=2880$$.

$$C^3_4$$ - choosing which 3 even positions out of 4 will be occupied by vowels (there are 4 even positions: 2nd, 4th, 6th and 8th and only 3 vowels);
$$3!$$ - # of different arrangements of these vowels on their even positions;
$$5!$$ - # of different arrangements of 8-3=5 other letters left.

Hope it helps.
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Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink]

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24 Dec 2015, 02:20
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Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink]

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12 Aug 2017, 08:21
Hello from the GMAT Club BumpBot!

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Re: In how many ways can the letters of the word "COMPUTER" be arranged?   [#permalink] 12 Aug 2017, 08:21
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# In how many ways can the letters of the word "COMPUTER" be arranged?

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