• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to $200 Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

## combinatorics

This topic has 2 expert replies and 1 member reply
Winner2013 Senior | Next Rank: 100 Posts
Joined
07 Jul 2013
Posted:
57 messages

#### combinatorics

Wed Jan 29, 2014 9:03 am
Q. A pod of 6 dolphins always swims single file, with 3 females at the front and 3
males in the rear. In how many different arrangements can the dolphins swim?

source - MGMAT strategy guide

I want to know where am i going wrong in my logic. Can someone help?

My logic :

6!
/ 3! * 3!

where am i going wrong?

thanks,

parveen110 Senior | Next Rank: 100 Posts
Joined
17 Jan 2014
Posted:
91 messages
7
Wed Jan 29, 2014 9:17 am
Winner2013 wrote:
Q. A pod of 6 dolphins always swims single file, with 3 females at the front and 3
males in the rear. In how many different arrangements can the dolphins swim?

source - MGMAT strategy guide

I want to know where am i going wrong in my logic. Can someone help?

My logic :

6!
/ 3! * 3!

where am i going wrong?

thanks,
According to the question the arrangement is like FFFMMM

Let's consider FFF as one item and MMM as another.

Now, the three female dolphins, FFF, may be arranged within themselves in 3! ways.
Similarly, the three male dolphins, MMM, may be arranged in 3! ways.

thereby giving, 3!x3!= 36 ways.

There are 3 red and 3 green marbles in a bag, they are drawn one by one and arranged in a row, assuming that all 6 marbles are drawn, determine the number of different arrangements.

Logic involved here is similar to what you have used, i.e, permutation of n things NOT all different.

### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
Joined
25 May 2010
Posted:
14182 messages
Followed by:
1820 members
13060
GMAT Score:
790
Wed Jan 29, 2014 1:07 pm
Winner2013 wrote:
Q. A pod of 6 dolphins always swims single file, with 3 females at the front and 3
males in the rear. In how many different arrangements can the dolphins swim?

source - MGMAT strategy guide

I want to know where am i going wrong in my logic. Can someone help?

My logic :

6!
/ 3! * 3!

where am i going wrong?

thanks,
Your solution would be correct for the following problem:
How many ways can the letters AAABBB be arranged?
Number of ways to arrange 6 distinct elements = 6!.
But the arrangement here includes 3 identical A's and 3 identical B's.
To account for the identical elements, we must divide by the number of ways each set of identical elements can be arranged.
The reason:
When the identical elements swap places, the arrangement doesn't change.
Thus, the number of ways to arrange AAABBB = 6!/(3!3!) = 20.
We divide by 3! to account for the 3 identical A's and by another 3! to account for the 3 identical B's.

In the posted problem:
The 3 female dolphins must occupy the 3 front positions, while the 3 male dolphins must occupy the 3 back positions.
In the 3 front positions, the number of ways to arrange the 3 female dolphins = 3!.
In the 3 back positions, the number of ways to arrange the 3 male dolphins = 3!.
To combine these options, we multiply:
3! * 3! = 36.
Since the dolphins are not identical, no division is necessary.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and long-distance.

Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

### GMAT/MBA Expert

Jeff@TargetTestPrep GMAT Instructor
Joined
09 Apr 2015
Posted:
1013 messages
Followed by:
13 members
39
Thu Dec 07, 2017 9:23 am
Winner2013 wrote:
Q. A pod of 6 dolphins always swims single file, with 3 females at the front and 3
males in the rear. In how many different arrangements can the dolphins swim?

A. 20
B. 36
C. 40
D. 18
E. 54
We are given that a pod of 6 dolphins always swims single file, with 3 females at the front and 3 males in the rear. Thus:

The number of ways to arrange the 3 female dolphins in the front is 3! = 3 x 2 x 1 = 6.

The number of ways to arrange the 3 male dolphins is in the rear is 3! = 3 x 2 x 1 = 6.

Thus, the number of ways to arrange all the dolphins is 6 x 6 = 36 ways.

_________________
Jeffrey Miller Head of GMAT Instruction

### Top First Responders*

1 GMATGuruNY 67 first replies
2 Rich.C@EMPOWERgma... 44 first replies
3 Brent@GMATPrepNow 40 first replies
4 Jay@ManhattanReview 25 first replies
5 Terry@ThePrinceto... 10 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 GMATGuruNY

The Princeton Review Teacher

132 posts
2 Rich.C@EMPOWERgma...

EMPOWERgmat

112 posts
3 Jeff@TargetTestPrep

Target Test Prep

95 posts
4 Scott@TargetTestPrep

Target Test Prep

92 posts
5 Max@Math Revolution

Math Revolution

91 posts
See More Top Beat The GMAT Experts