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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

On how many ways can the letters of the word "COMPUTER" be a [#permalink]

Show Tags

25 Jun 2007, 13:04

2

This post received KUDOS

13

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

73% (01:52) correct 27% (07:06) wrong based on 64 sessions

HideShow timer Statistics

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

1) Without any restrictions. 2) M must always occur at the third place. 3) All the vowels are together. 4) All the vowels are never together. 5) Vowels occupy the even positions[/b]
_________________

Thank you. somehow i can't be sure of my answers, when it comes to arrangement possibilities or probability calculation. Though i got first 4 correct here

Re: PS - On how many ways can the letters of the word... [#permalink]

Show Tags

19 Feb 2012, 03:07

3

This post received KUDOS

BDSunDevil wrote:

Can someone check for 4 and 5: i keep getting 4: 5!*6p3=2400 5. 720*4=2880

4) All the vowels are never together. This is equivalent to (All possibilities - All the vowels are ALWAYS together) = 8! - 6!3!

5) Vowels occupy the even positions. let us consider the following: first 3 vowels placing together in even positions: -O-U-E-- -O---U-E ---O-U-E Like this, at any point in time we have 4 positions to fill with 3 letters. Hence no. of ways will be 4P3 = 4!

Remaining 5 positions can be filled by 5!

Hence total ways = 4! x 5!

Hope this is clear. (if you like, give me kudos, please )
_________________

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

1. Without any restrictions: Since all letters in the word "COMPUTER" are distinct then the # of arrangements is 8!.

2. M must always occur at the third place: M is fixed at the third place, other 7 distinct letters can be arranged in 7! ways,

3. All the vowels are together: Consider three vowels as one unit: {OEU}. Thus we'll have total of 6 units: {OEU}{C}{M}{P}{T}{R}, which can be arranged in 6! ways. Three vowels within their unit can be arranged in 3! ways. Total: 6!*3!.

4. All the vowels are never together: Total minus restriction: 8!-6!*3!.

5. Vowels occupy the even positions (the 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.

Re: On how many ways can the letters of the word "COMPUTER" be a [#permalink]

Show Tags

19 Feb 2012, 20:24

1

This post received KUDOS

Apex231 wrote:

4. All the vowels are never together:

I did this -

3 vowels and 5 non-vowels.

number of ways to arrange 5 non-vowels = 5! (represented by | below).

-|-|-|-|-|-

Now there are 6 places (represented by -) that vowels can occupy so that they are not together. Number of ways vowels can be arranged = 6P3 = 120

total number of ways = 120 * 5! = 14400.

What am i doing wrong?

Question says "ALL the vowels not together". So, you have excluded valid cases like COMPTUER, CMPOUTER

One thing: it is generally a good practice to find the probability of something to occur and then subtract it from 1 to find for the same thing to not occur. This way, we don;t commit above mistakes.

Re: On how many ways can the letters of the word "COMPUTER" be a [#permalink]

Show Tags

26 Sep 2017, 02:58

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.
_________________