It is currently 21 Oct 2017, 02:12

### 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 : word DELETED

Author Message
Senior Manager
Joined: 06 Jul 2007
Posts: 275

Kudos [?]: 53 [0], given: 0

### Show Tags

20 Mar 2009, 16:09
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.

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

Let each different arrangement of all the letters of DELETED be called a word. In how many of these words will the D's be separated?

I can get the number by first finding the total number of words which is 7!/(3!*2!) = 420 and then subtracting from it the total number of words that has D's together (this number is 6!/3! = 120). Can someone explain how I can find the result through regular counting process?

Kudos [?]: 53 [0], given: 0

Director
Joined: 01 Apr 2008
Posts: 875

Kudos [?]: 843 [0], given: 18

Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: Permutation : word DELETED [#permalink]

### Show Tags

27 Mar 2009, 11:24
420 is correct.
now if we take DD as one entity then we have 6! ways, but within this D is repeating so we get 6!/2! ...why do we take 6!/3! . Please explain.
sanjay_gmat wrote:
Let each different arrangement of all the letters of DELETED be called a word. In how many of these words will the D's be separated?

I can get the number by first finding the total number of words which is 7!/(3!*2!) = 420 and then subtracting from it the total number of words that has D's together (this number is 6!/3! = 120). Can someone explain how I can find the result through regular counting process?

Kudos [?]: 843 [0], given: 18

Senior Manager
Joined: 06 Jul 2007
Posts: 275

Kudos [?]: 53 [0], given: 0

Re: Permutation : word DELETED [#permalink]

### Show Tags

27 Mar 2009, 14:03
Economist wrote:
420 is correct.
now if we take DD as one entity then we have 6! ways, but within this D is repeating so we get 6!/2! ...why do we take 6!/3! . Please explain.
sanjay_gmat wrote:
Let each different arrangement of all the letters of DELETED be called a word. In how many of these words will the D's be separated?

I can get the number by first finding the total number of words which is 7!/(3!*2!) = 420 and then subtracting from it the total number of words that has D's together (this number is 6!/3! = 120). Can someone explain how I can find the result through regular counting process?

Well, the six elements in second case (both D's together) are :

1 - DD
2 - E
3 - E
4 - E
5 - L
6 - T

in this group, there are 3 repetitive elements, hence total number of permutations = 6!/3!.

I don't think you need to divide by 2! because the 2Ds are considered one single group.

Kudos [?]: 53 [0], given: 0

Manager
Joined: 19 Aug 2006
Posts: 239

Kudos [?]: 13 [0], given: 0

Re: Permutation : word DELETED [#permalink]

### Show Tags

27 Mar 2009, 21:13
sanjay_gmat wrote:
Let each different arrangement of all the letters of DELETED be called a word. In how many of these words will the D's be separated?

I can get the number by first finding the total number of words which is 7!/(3!*2!) = 420 and then subtracting from it the total number of words that has D's together (this number is 6!/3! = 120). Can someone explain how I can find the result through regular counting process?

I'm probably missing something, but could you please confirm you answer is 120?
Because I got 60 as the final answer.

Kudos [?]: 13 [0], given: 0

Manager
Joined: 02 Mar 2009
Posts: 134

Kudos [?]: 55 [0], given: 0

Re: Permutation : word DELETED [#permalink]

### Show Tags

06 Apr 2009, 23:23
So..Sanjay..Is the answer 420-120 = 300 ways that the D's will be separated?

Kudos [?]: 55 [0], given: 0

Re: Permutation : word DELETED   [#permalink] 06 Apr 2009, 23:23
Display posts from previous: Sort by