GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Mar 2019, 17:03

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 16 Apr 2010
Posts: 197
In how many ways can the letters of the word "COMPUTER" be arranged if  [#permalink]

### Show Tags

Updated on: 26 Feb 2019, 04:45
2
00:00

Difficulty:

55% (hard)

Question Stats:

42% (01:50) correct 58% (02:04) wrong based on 19 sessions

### HideShow timer Statistics

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.
Intern
Joined: 03 Mar 2010
Posts: 37
Re: In how many ways can the letters of the word "COMPUTER" be arranged if  [#permalink]

### Show Tags

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.
_________________

Hardworkingly, you like my post, so kudos me.

##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 53657
Re: In how many ways can the letters of the word "COMPUTER" be arranged if  [#permalink]

### Show Tags

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.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 53657
In how many ways can the letters of the word "COMPUTER" be arranged if  [#permalink]

### Show Tags

12 Jan 2012, 06:27
Similar question: https://gmatclub.com/forum/in-how-many- ... 47764.html
_________________
Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 278
Re: In how many ways can the letters of the word "COMPUTER" be arranged?  [#permalink]

### Show Tags

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

Math Expert
Joined: 02 Sep 2009
Posts: 53657
Re: In how many ways can the letters of the word "COMPUTER" be arranged?  [#permalink]

### Show Tags

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
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 10130
Re: In how many ways can the letters of the word "COMPUTER" be arranged if  [#permalink]

### Show Tags

08 Mar 2019, 06:13
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: In how many ways can the letters of the word "COMPUTER" be arranged if   [#permalink] 08 Mar 2019, 06:13
Display posts from previous: Sort by