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

 It is currently 28 May 2017, 02:25

### 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

# Out of seven models, all of different heights, five models

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Manager
Joined: 21 Dec 2005
Posts: 102
Followers: 1

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

Out of seven models, all of different heights, five models [#permalink]

### Show Tags

02 Apr 2006, 18:49
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Out of seven models, all of different heights, five models will be chosen to pose for a photograph. If the five models are to stand in a line from shortest to tallest, and the fourth-tallest and sixth-tallest models cannot be adjacent, how many different arrangements of five models are possible?

Thanks
Senior Manager
Joined: 22 Nov 2005
Posts: 474
Followers: 2

Kudos [?]: 20 [0], given: 0

### Show Tags

02 Apr 2006, 20:17
Here is the explanation.
Total number of ways models can be arranged = 7C5

Total number of ways 4th and 6th models can be chosen together = 4C3
Here we have to exclude 5th modle so only 4 models are left

hence total number of ways = 7C5 - 4C3

=17
Manager
Joined: 21 Dec 2005
Posts: 102
Followers: 1

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

### Show Tags

02 Apr 2006, 20:30
Thanks

Could you please explain why after choosing five models, we have the sixth model and why is it that its 4C3. What does 4C3 mean in this case..are we choosing 4 out of 3 why so?

Thanks
VP
Joined: 20 Sep 2005
Posts: 1018
Followers: 3

Kudos [?]: 36 [0], given: 0

### Show Tags

02 Apr 2006, 22:14
The constraint is "when we choose 4 and 6, we can't choose 5"...that leaves with choosing 3 models from the remaining 4.

jodeci wrote:
Thanks

Could you please explain why after choosing five models, we have the sixth model and why is it that its 4C3. What does 4C3 mean in this case..are we choosing 4 out of 3 why so?

Thanks
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5045
Location: Singapore
Followers: 31

Kudos [?]: 376 [0], given: 0

### Show Tags

03 Apr 2006, 04:39
Total number of ways to pick 5 models = 7C5 = 7!/5!2! = 21 ways

Constraint: 6th talles and 4th tallest cannot be adjacent to each other:

Number of ways 64 are adjacent to each other:

Can be 64321 --> 1 way
Can be 764XX --> 3C2 ways = 3!/2!1! = 3 ways

Total = 1 + 3 = 4

# of different arrangements = 21-4 = 17
Manager
Joined: 21 Dec 2005
Posts: 102
Followers: 1

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

### Show Tags

04 Apr 2006, 12:32
Can be 64321 --> 1 way

How can we 3C2 yet it is an arrangement.

I only find 76432, 76421 as the only viable options. I do not know about 764231 Please explain why we have this

Can be 764XX --> 3C2 ways = 3!/2!1! = 3 ways

Thanks
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5045
Location: Singapore
Followers: 31

Kudos [?]: 376 [0], given: 0

### Show Tags

04 Apr 2006, 17:47
jodeci wrote:
Can be 64321 --> 1 way

How can we 3C2 yet it is an arrangement.

I only find 76432, 76421 as the only viable options. I do not know about 764231 Please explain why we have this

Can be 764XX --> 3C2 ways = 3!/2!1! = 3 ways

Thanks

Because the last two places can be taken by any of the 3 remaining models who are shorter than 4. We cannot take 5 as that would mean model 6 and model 4 would not be standing side by side.

Since we have 3 models and only 2 places, the number of ways to pick a pair of 2 models from a pool of 3, is 3C2.

In case you were interested, the 3 ways to do it:

76432
76431
76421
Senior Manager
Joined: 24 Jan 2006
Posts: 252
Followers: 1

Kudos [?]: 5 [0], given: 0

### Show Tags

04 Apr 2006, 20:16
I had very long way of doing this thanks for quick explanations ywilfred.
04 Apr 2006, 20:16
Display posts from previous: Sort by

# Out of seven models, all of different heights, five models

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.