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

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In how many ways can the letters of the word "COMPUTER" be arranged if  [#permalink]

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Updated on: 26 Feb 2019, 04:45
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00:00

Difficulty:

55% (hard)

Question Stats:

51% (01:49) correct 49% (02:18) wrong based on 41 sessions

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In how many ways can the letters of the word "COMPUTER" be arranged if vowels occupy the even positions?

A. 480
B. 576
C. 720
D. 960
E. 2880

Originally posted by jakolik on 27 Jul 2010, 20:50.
Last edited by Bunuel on 26 Feb 2019, 04:45, edited 2 times in total.
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Joined: 02 Sep 2009
Posts: 58340
Re: In how many ways can the letters of the word "COMPUTER" be arranged if  [#permalink]

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28 Jul 2010, 00:12
jakolik wrote:
Hello,

What is the shortest and most systematic way of solving the below question?

In how many ways can the letters of the word "COMPUTER" be arranged if vowels occupy the even positions?

regards,
Jack

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 if  [#permalink]

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28 Jul 2010, 00:18
4
1
The word COMPUTER consists of 8 letters of which 3 vowels. All letters are distinc.
First, put 3 vowels into 3 of the positions 2, 4, 6, and 8. There are 4*3*2=24 ways.
Second, once the positions of the 3 vowels are determined, we have to put the 5 other letters into the remaining positions. There are 5*4*3*2*1=120 ways.
Therefore, there are a total of 120*24=2880 ways.
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##### General Discussion
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In how many ways can the letters of the word "COMPUTER" be arranged if  [#permalink]

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12 Jan 2012, 06:27
Similar question: https://gmatclub.com/forum/in-how-many- ... 47764.html
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Re: In how many ways can the letters of the word "COMPUTER" be arranged?  [#permalink]

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20 Dec 2017, 04:43
Bunuel wrote:
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.

hi man

I am getting 5 even positions

| C | M | P | T | R |
O E O E O E O E O E O

separating the consonants, I have inserted the vowels into the gaps

what is wrong here, please do say to me, man

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Joined: 02 Sep 2009
Posts: 58340
Re: In how many ways can the letters of the word "COMPUTER" be arranged?  [#permalink]

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20 Dec 2017, 05:39
gmatcracker2017 wrote:
Bunuel wrote:
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.

hi man

I am getting 5 even positions

| C | M | P | T | R |
O E O E O E O E O E O

separating the consonants, I have inserted the vowels into the gaps

what is wrong here, please do say to me, man

There are 8 letters in "COMPUTER" there are 4 even positions: 1st-2nd-3rd-4th-5th-6th-7th-8th
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Re: In how many ways can the letters of the word "COMPUTER" be arranged if  [#permalink]

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02 Jun 2019, 02:06
1
jakolik wrote:
In how many ways can the letters of the word "COMPUTER" be arranged if vowels occupy the even positions?

A. 480
B. 576
C. 720
D. 960
E. 2880

COMPUTER
Vowels = OUE ; can be positioned in 4c3 *3! ways = 24
and others 5! ways ; 120
so total 120*24 ; 2880
IMO E
Re: In how many ways can the letters of the word "COMPUTER" be arranged if   [#permalink] 02 Jun 2019, 02:06
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