How many ways are possible to arrange A, B, C, C, and D with : PS Archive
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 10 Dec 2016, 10:41

### 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

# How many ways are possible to arrange A, B, C, C, and D with

Author Message
Director
Joined: 05 Jan 2008
Posts: 701
Followers: 4

Kudos [?]: 405 [1] , given: 0

How many ways are possible to arrange A, B, C, C, and D with [#permalink]

### Show Tags

20 Apr 2008, 11:48
1
KUDOS
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

How many ways are possible to arrange A, B, C, C, and D with two "C" being separated by at least one letter?
_________________

Persistence+Patience+Persistence+Patience=G...O...A...L

Intern
Joined: 02 Apr 2008
Posts: 37
Followers: 0

Kudos [?]: 11 [1] , given: 0

### Show Tags

20 Apr 2008, 11:56
1
KUDOS
I get 36

Perms:
CACBD - 6 possibilities
CABCD - 6
CABDC-6
ACBCD-6
ACBDC-6
ABCDC-6

6*6 = 36

However if Cs are distinct (which is probably not what the question implies), the answer would be 72.
Manager
Joined: 09 Apr 2008
Posts: 60
Concentration: Strategy, Operations
Schools: CBS '15 (A)
Followers: 0

Kudos [?]: 14 [1] , given: 0

### Show Tags

20 Apr 2008, 11:57
1
KUDOS
C _ C _ _
C _ _ C _
C _ _ _ C
_ C _ C _
_ C _ _ C
_ _ C _ C

In each of these, we have 3 blanks, the contents of which are completely up for variation (thus it is a factorial).

3! = 3*2*1 = 6 possibilities for each of the patterns above

6*6 = 36

Another note:
--Since the C's are the same, we don't need to account for switching the two C's in each case above.
_________________

"The price of anything is the amount of life you exchange for it." -Thoreau

Senior Manager
Joined: 19 Apr 2008
Posts: 320
Followers: 3

Kudos [?]: 77 [1] , given: 0

### Show Tags

20 Apr 2008, 22:03
1
KUDOS
I get 96 (5!-4!) , is that correct?

5! = number of ways to arrange A,B,C,C,D
4! = assuming CC are consecutive

so Number of ways such that C,C are atlease one space apart is 5!-4!=96
CEO
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 531

Kudos [?]: 3457 [1] , given: 360

### Show Tags

20 Apr 2008, 22:15
1
KUDOS
Expert's post
rpmodi wrote:
I get 96 (5!-4!) , is that correct?

5! = number of ways to arrange A,B,C,C,D
4! = assuming CC are consecutive

so Number of ways such that C,C are atlease one space apart is 5!-4!=96

5! corresponds to 5 different things but here we have the same two things and 3 different. So, the correct total number of ways to arrange A,B,C,C,D will be 5!/2. ($$A,B,C_1,C_2,D$$ and $$A,B,C_2,C_1,D$$ is the same combination)

5!/2-4!=60-24=36
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Senior Manager
Joined: 19 Apr 2008
Posts: 320
Followers: 3

Kudos [?]: 77 [0], given: 0

### Show Tags

20 Apr 2008, 22:16
sorry , my answer is 36 as well

it should be 5!/2 - 4! ( 5!/2 since we have a repetition of C )
Re: PS: Possible ways   [#permalink] 20 Apr 2008, 22:16
Display posts from previous: Sort by