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

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jakolik
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In how many ways can the letters of the word "COMPUTER" be arranged if [#permalink] New post   Updated on: 26 Feb 2019, 04:45
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59% (02:05) correct 41% (02:10) wrong based on 193 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
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E

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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Bunuel
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Re: In how many ways can the letters of the word "COMPUTER" be arranged if [#permalink] New post   28 Jul 2010, 00:12
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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] New post   28 Jul 2010, 00:18
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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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In how many ways can the letters of the word "COMPUTER" be arranged if [#permalink] New post   12 Jan 2012, 06:27
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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] New post   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
please help me out

| 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

thanks in advance
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Re: In how many ways can the letters of the word "COMPUTER" be arranged? [#permalink] New post   20 Dec 2017, 05:39
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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
please help me out

| 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

thanks in advance


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] New post   02 Jun 2019, 02:06
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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
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Re: In how many ways can the letters of the word "COMPUTER" be arranged if [#permalink] New post   05 Nov 2020, 11:57
Bunuel

In GMAT exam, if we ran into similar questions but with larger factorials , how to calculate the factorials of a large number quickly within 2 minute time frame?

While solving a similar question, i ran into a bigger number such as this 10C4∗2!∗4!∗7!2!=25,401,600. I took longer time to reach the solution. Is there a shortcut or simpler steps to get final answer without involving larger multiplications ?

Thanks much
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Re: In how many ways can the letters of the word "COMPUTER" be arranged if [#permalink] New post   10 Nov 2020, 07:03
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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

Solution:

We see that the word “COMPUTER” has 8 letters and 3 vowels: O, U and E. Since there are 4 even positions (i.e, 2nd, 4th, 6th and 8th positions) and order matters, the 3 vowels can occupy the 4 even positions in 4P3 = 4 x 3 x 2 = 24 ways, and the 5 consonants can occupy the remaining positions (not occupied by a vowel) in 5! = 120 ways. Therefore, there are a total of 24 x 120 = 2880 ways to arrange the letters in the word “COMPUTER” if the vowels occupy the even positions.

Answer: E
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Re: In how many ways can the letters of the word "COMPUTER" be arranged if [#permalink] New post   05 Nov 2022, 10:47
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Re: In how many ways can the letters of the word "COMPUTER" be arranged if [#permalink]
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