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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
Posts: 142
Location: India
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, 06:08
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Question Stats:

100% (01:14) correct 0% (00:00) wrong based on 22 sessions

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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???
_________________

just one more month for exam...

Math Expert
Joined: 02 Sep 2009
Posts: 53063
Re: In how many ways can the letters of the word "COMPUTER" be arranged?  [#permalink]

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12 Jan 2012, 05:27
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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Joined: 23 Jun 2017
Posts: 11
Re: In how many ways can the letters of the word "COMPUTER" be arranged?  [#permalink]

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05 Dec 2017, 05:05
1
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.

Isn't it 4C3*3!*5!
Math Expert
Joined: 02 Sep 2009
Posts: 53063
Re: In how many ways can the letters of the word "COMPUTER" be arranged?  [#permalink]

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05 Dec 2017, 05:18
1
Varun121595 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.

Isn't it 4C3*3!*5!

Isn't it EXACTLY what's written in the solution?
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Joined: 24 Jul 2017
Posts: 5
Re: In how many ways can the letters of the word "COMPUTER" be arranged?  [#permalink]

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08 Dec 2017, 20:31
Bunuel wrote:

Isn't it EXACTLY what's written in the solution?

I'm guessing that's a typo. You wrote 3C4 (I'm not sure if that's even possible?)

But, from your explanation-- "$$C^3_4$$ - 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); " it's quite clear, you meant 4C3

Math Expert
Joined: 02 Sep 2009
Posts: 53063
Re: In how many ways can the letters of the word "COMPUTER" be arranged?  [#permalink]

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08 Dec 2017, 21:34
karnikabansal wrote:
Bunuel wrote:

Isn't it EXACTLY what's written in the solution?

I'm guessing that's a typo. You wrote 3C4 (I'm not sure if that's even possible?)

But, from your explanation-- "$$C^3_4$$ - 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); " it's quite clear, you meant 4C3

4C3, $$C^3_4$$, $$C^4_3$$ mean the same choosing 3 out of 4 (just different ways of writing). Could out be 4 out of 3?
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Posts: 273
Re: In how many ways can the letters of the word "COMPUTER" be arranged?  [#permalink]

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20 Dec 2017, 03:43
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

Math Expert
Joined: 02 Sep 2009
Posts: 53063
Re: In how many ways can the letters of the word "COMPUTER" be arranged?  [#permalink]

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20 Dec 2017, 04:39
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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Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 273
Re: In how many ways can the letters of the word "COMPUTER" be arranged?  [#permalink]

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20 Dec 2017, 05:48
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

okay man
thanks a lot
take care
Re: In how many ways can the letters of the word "COMPUTER" be arranged?   [#permalink] 20 Dec 2017, 05:48
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