Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 22 May 2017, 16:26

### 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 different possible arrangements can be obtained

Author Message
Manager
Joined: 12 Sep 2006
Posts: 91
Followers: 1

Kudos [?]: 2 [0], given: 0

How many different possible arrangements can be obtained [#permalink]

### Show Tags

02 Oct 2006, 02:27
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 2 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 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 Iâ€™s?
1. 360
2. 720
3. 900
4. 1,800
5. 5,040
VP
Joined: 25 Jun 2006
Posts: 1167
Followers: 3

Kudos [?]: 157 [0], given: 0

### Show Tags

02 Oct 2006, 02:39
.
.
.
.
.
.

find those permutations that have no letters between I and subtract it from the total permutation.

1. total permutation: 7!
2. permutations to subtract from 1, just treat two I's as one element. it is 6!. tricky here: since I am going to subtract it from 7!, i need to consider the permutations of 2 I's together. so this intermediate result is 2*6!.
3. 7! - 2*6! is the rest of the permutations. but there are 2 T's, so the order does not matter for T. then divide 7!-2*6! by 2.

(7!-2*6!)/2 = 1800
Manager
Joined: 12 Sep 2006
Posts: 91
Followers: 1

Kudos [?]: 2 [0], given: 0

### Show Tags

02 Oct 2006, 06:35
Tennis ball,

how to arrive to this??
VP
Joined: 25 Jun 2006
Posts: 1167
Followers: 3

Kudos [?]: 157 [0], given: 0

### Show Tags

02 Oct 2006, 17:46
Sorry. My previous one was wrong. it is 900.

this is the calculation:

1. the total number of arrangements is :

7!/(2x2). because Ts and Is don't have effects on permutation.

2. find those that two Is are together. Just treat the 2 Is as 1.

6!/2, Ts don't have effects, so divide 6! by 2.

then 7!/4 - 6!/2 = 900.

Guess my first thinking is too complex.
02 Oct 2006, 17:46
Display posts from previous: Sort by