It is currently 18 Oct 2017, 11:43

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Permutation and Combination

Author Message
Intern
Joined: 18 Sep 2005
Posts: 7

Kudos [?]: [0], given: 0

Location: Delhi

### Show Tags

19 Sep 2005, 23:29
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Hi

Help me with the P&C question below, tell simple way. Tell me links where I can find more of P&C stuff.

In how many ways can the letters of the word ABACUS be
rearranged such that the vowels always appear together?

A. 6!/2!
B. 3!*3!
C. 4!/2!
D. 4! *3!/2!
E. 3!*3!/2

Thanks

Kudos [?]: [0], given: 0

Director
Joined: 13 Nov 2003
Posts: 788

Kudos [?]: 61 [0], given: 0

Location: BULGARIA

### Show Tags

20 Sep 2005, 04:26
ABACUS has 6 letters, 3 vowels and 3 consonants .Take all the vowels as one unit then u have 4 elements- each of the consonants and a group of 3 vowels. This can be ordered in 4! ways. But don't forget that the group of 3 vowels can have 3! orderings within the group. Or we have 4!x3! and finally cause u have 2-A's you need to divide the whole product by2!, or your ans should be (4!x3!)/2! or option D)

Kudos [?]: 61 [0], given: 0

Senior Manager
Joined: 27 Aug 2005
Posts: 331

Kudos [?]: 194 [0], given: 0

### Show Tags

20 Sep 2005, 07:11
Same here, intuitively. 72 is the answer.

There are 4 places where the string of 3 vowels can appear:
VVVCCC
CVVVCC
CCVVVC
CCCVVV

The string of vowels can be arranged in 3 ways (because two of the letters are identical As):
AAU
AUA
UAA

The string of consonants can be arranged in 6 ways (because the letters are all different):
BCS
BSC
CBS
CSB
SCB
SBC

4x6x3 = 72 = 4! *3!/2! or D.

Kudos [?]: 194 [0], given: 0

Intern
Joined: 19 Aug 2005
Posts: 41

Kudos [?]: 4 [0], given: 0

### Show Tags

20 Sep 2005, 08:43
D.. same explanation as others

For P&Cs i borrowed a book called Probability without tears from my local library and got help. i guess if u have time u can try gettin a book too

Kudos [?]: 4 [0], given: 0

Intern
Joined: 18 Sep 2005
Posts: 7

Kudos [?]: [0], given: 0

Location: Delhi

### Show Tags

20 Sep 2005, 22:22
BG wrote:
ABACUS has 6 letters, 3 vowels and 3 consonants .Take all the vowels as one unit then u have 4 elements- each of the consonants and a group of 3 vowels. This can be ordered in 4! ways. But don't forget that the group of 3 vowels can have 3! orderings within the group. Or we have 4!x3! and finally cause u have 2-A's you need to divide the whole product by2!, or your ans should be (4!x3!)/2! or option D)

Thank you very much for the simple explanation

Kudos [?]: [0], given: 0

Intern
Joined: 18 Sep 2005
Posts: 7

Kudos [?]: [0], given: 0

Location: Delhi

### Show Tags

20 Sep 2005, 22:29
coffeeloverfreak wrote:
Same here, intuitively. 72 is the answer.

There are 4 places where the string of 3 vowels can appear:
VVVCCC
CVVVCC
CCVVVC
CCCVVV

The string of vowels can be arranged in 3 ways (because two of the letters are identical As):
AAU
AUA
UAA

The string of consonants can be arranged in 6 ways (because the letters are all different):
BCS
BSC
CBS
CSB
SCB
SBC

4x6x3 = 72 = 4! *3!/2! or D.

Thank you very much.

Kudos [?]: [0], given: 0

20 Sep 2005, 22:29
Display posts from previous: Sort by