GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 30 Mar 2020, 15:46

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

How many different possible arrangements can be obtained from the lett

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 08 Jan 2015
Posts: 25
How many different possible arrangements can be obtained from the lett  [#permalink]

Show Tags

New post 30 Mar 2015, 10:30
12
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

61% (02:15) correct 39% (02:27) wrong based on 121 sessions

HideShow timer Statistics

How many different possible arrangements can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's?

A. 360
B. 720
C. 900
D. 1800
E. 5040
Senior Manager
Senior Manager
User avatar
Joined: 07 Aug 2011
Posts: 492
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
Re: How many different possible arrangements can be obtained from the lett  [#permalink]

Show Tags

New post 30 Mar 2015, 10:36
3
Awli wrote:
How many different possible arrangements can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's?

A. 360
B. 720
C. 900
D. 1800
E. 5040



A= all possible permutations = \(\frac{7!}{2!2!}\)
B= permutations with II together = \(\frac{6!}{2!}\)

A-B = 900
Intern
Intern
avatar
Joined: 08 Jan 2015
Posts: 25
Re: How many different possible arrangements can be obtained from the lett  [#permalink]

Show Tags

New post 30 Mar 2015, 10:43
Could you explain me in detail why B is 6! / 2! ?

Thank you.
Senior Manager
Senior Manager
User avatar
Joined: 07 Aug 2011
Posts: 492
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
Re: How many different possible arrangements can be obtained from the lett  [#permalink]

Show Tags

New post 30 Mar 2015, 11:06
2
Awli wrote:
Could you explain me in detail why B is 6! / 2! ?

Thank you.



yes sure.

we have to find those cases where we have at least 1 Character between two I I , if we find those cases where there is no character between two I I and subtract this number from total permutations we will be left with those cases where there are 1 or more characters between two I I .

assume II as one unit so we have total 6 characters G M A T T (II)
total ways to arrange these 6 letters is \(\frac{6!}{2!}\) , as we have 2 Ts so we have to divide 6! by 2! .

hope the explanation is helpful to you !
SVP
SVP
avatar
B
Joined: 06 Nov 2014
Posts: 1865
Re: How many different possible arrangements can be obtained from the lett  [#permalink]

Show Tags

New post 31 Mar 2015, 01:50
1
2
Awli wrote:
How many different possible arrangements can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's?

A. 360
B. 720
C. 900
D. 1800
E. 5040


There are 7 letters G, M, A, T, I, I, and T with I and T repeated twice.
Hence total arrangements/permutations of letters = 7!/(2! * 2!) = 1260.

Now, let us say that the two "I" are always together.
So now we have 6 letters G, M, A, T, II, T with T repeated twice.
Hence total arrangements/permutations of letters = 6!/(2!) = 360.

Required arrangements = 1260 - 360
= 900
Hence option (C).

--
Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimus-prep.com/gmat-on-demand-course
Intern
Intern
avatar
Joined: 08 Jan 2015
Posts: 25
Re: How many different possible arrangements can be obtained from the lett  [#permalink]

Show Tags

New post 31 Mar 2015, 01:56
Lucky2783 wrote:
Awli wrote:
Could you explain me in detail why B is 6! / 2! ?

Thank you.



yes sure.

we have to find those cases where we have at least 1 Character between two I I , if we find those cases where there is no character between two I I and subtract this number from total permutations we will be left with those cases where there are 1 or more characters between two I I .

assume II as one unit so we have total 6 characters G M A T T (II)
total ways to arrange these 6 letters is \(\frac{6!}{2!}\) , as we have 2 Ts so we have to divide 6! by 2! .

hope the explanation is helpful to you !



Yes, it's been very helpful. Thank you very much!
Manager
Manager
avatar
Joined: 24 May 2013
Posts: 73
GMAT ToolKit User
Re: How many different possible arrangements can be obtained from the lett  [#permalink]

Show Tags

New post 19 Mar 2016, 11:04
1
How many different possible arrangements can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's?

_ _ _ _ _ _ _
Total ways for arranging without restriction = 7!/ (2!2!) { 2! is becoz of two T's and other 2! for two I's)
Restriction : atleast one character between I's = Possible ways - both I's together i.e.o character between I's

_ _ _ _ _ (I I)
Both I's Together = 6! (Assuming 2 I's as one unit) /2!(for 2 T's) * 2! (No of arrangements of 2 I's)/2! (for 2 I's)
=6!/2!

Therefore ans = 7!/ (2!2!) -6!/2! = 900
HENCE C.

A. 360
B. 720
C. 900
D. 1800
E. 5040
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14448
Re: How many different possible arrangements can be obtained from the lett  [#permalink]

Show Tags

New post 03 Jul 2019, 13:13
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.
_________________
GMAT Club Bot
Re: How many different possible arrangements can be obtained from the lett   [#permalink] 03 Jul 2019, 13:13
Display posts from previous: Sort by

How many different possible arrangements can be obtained from the lett

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne