Six children - A, B, C, D, E, and F - are going to sit in six chairs in a row. Child E must be somewhere to the left of child F. How many possible configurations are there for the children?

A)60

B)180

C)240

D)360

E)720

OA

D

## Six children - A, B, C, D, E, and F

##### This topic has expert replies

- gmat_guy666
- Senior | Next Rank: 100 Posts
**Posts:**48**Joined:**23 Apr 2013**Thanked**: 6 times

### GMAT/MBA Expert

- [email protected]
- GMAT Instructor
**Posts:**15885**Joined:**08 Dec 2008**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1267 members**GMAT Score:**770

First, let's IGNORE the rule about child E seated somewhere to the left of child F.gmat_guy666 wrote:Six children - A, B, C, D, E, and F - are going to sit in six chairs in a row. Child E must be somewhere to the left of child F. How many possible configurations are there for the children?

A)60

B)180

C)240

D)360

E)720

When we ignore the rule, we can arrange the 6 children in 6! ways (= 720 ways)

Now recognize that, in HALF of those 720 arrangements, child E is seated somewhere to the

**LEFT**of child F, and in the other HALF of those 720 arrangements, child E is seated somewhere to the

**RIGHT**of child F.

So, the number of arrangements where child E is seated somewhere to the left of child F = (1/2)720 = 360

Answer: D

NOTE: This question is almost identical to this one: https://www.beatthegmat.com/counting-six ... tml#198825

Cheers,

Brent

### GMAT/MBA Expert

- [email protected]
- GMAT Instructor
**Posts:**15885**Joined:**08 Dec 2008**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1267 members**GMAT Score:**770

- https://www.beatthegmat.com/permutation-t261691.html

- https://www.beatthegmat.com/vowels-and-c ... 49946.html

- https://www.beatthegmat.com/how-many-pos ... 77574.html

Cheers,

Brent

### GMAT/MBA Expert

- [email protected]
- Elite Legendary Member
**Posts:**10392**Joined:**23 Jun 2013**Location:**Palo Alto, CA**Thanked**: 2867 times**Followed by:**508 members**GMAT Score:**800

Brent's explanation is arguably the most efficient way to get to the correct answer. Here's a more drawn-out explanation for the correct answer:

We're given 6 spots:

_ _ _ _ _ _

And we have to put a child in each spot; E MUST be to the left of F though. Here's one possible way that this can occur:

E F _ _ _ _

In this option, any of the remaining 4 children can be placed in each of the 4 remaining spots, so we have....

E F (4)(3)(2)(1) = 24 options with E and F in the 1st and 2nd spots, respectively.

This pattern will occur over-and-over. For example....If E and F were in other places....

(4)E(3)(2)F(1) = 24 options with E and F in the 2nd and 5th spots, respectively.

So we really just need all of the possible placements for E and F, then we can multiply that result by 24...

While this is not necessarily the most efficient way to approach this task, the work isn't that hard....

E F _ _ _ _

E _ F _ _ _

E _ _ F _ _

E _ _ _ F _

E _ _ _ _ F

_ E F _ _ _

_ E _ F _ _

_ E _ _ F _

_ E _ _ _ F

_ _ E F _ _

_ _ E _ F _

_ _ E _ _ F

_ _ _ E F _

_ _ _ E _ F

_ _ _ _ E F

15 possible placements for E and F (given the restriction that E must be to the left of F).

15 x 24 = 360

Final Answer: D

GMAT assassins aren't born, they're made,

Rich

- GMATGuruNY
- GMAT Instructor
**Posts:**15533**Joined:**25 May 2010**Location:**New York, NY**Thanked**: 13060 times**Followed by:**1901 members**GMAT Score:**790

One more approach:gmat_guy666 wrote:Six children - A, B, C, D, E, and F - are going to sit in six chairs in a row. Child E must be somewhere to the left of child F. How many possible configurations are there for the children?

A)60

B)180

C)240

D)360

E)720

There are no constraints on A, B, C, and D.

Number of options for A = 6. (Any of the 6 chairs.)

Number of options for B = 5. (Any of the 5 remaining chairs.)

Number of options for C = 4. (Any of the 4 remaining chairs.)

Number of options for D = 3. (Any of the 3 remaining chairs.)

Of the 2 remaining chairs, the one most to the left must be occupied by E, since E must sit to the left of F.

Number of options for E = 1. (The chair most to the left.)

Number of options for F = 1. (Only 1 chair remains.)

To combine the options above, we multiply:

6*5*4*3*1*1 = 360.

The correct answer is D.

Mitch Hunt

Private Tutor for the GMAT and GRE

[email protected]

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.

For more information, please email me at [email protected].

Student Review #1

Student Review #2

Student Review #3

Private Tutor for the GMAT and GRE

[email protected]

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.

For more information, please email me at [email protected].

Student Review #1

Student Review #2

Student Review #3

- GMATinsight
- Legendary Member
**Posts:**1097**Joined:**10 May 2014**Location:**New Delhi, India**Thanked**: 205 times**Followed by:**24 members

An Alternate methods is:

Select two places for B and E and there is only 1 way for them to sit on those chair, the chairs for B and E can be selected in 6C2 ways = 15

Now remaining 4 chairs can be occupied by other 4 people in 4! ways = 24 ways

Total ways : 6C2 x 4! = 15 x 24 = 360

Answer: Option D

Select two places for B and E and there is only 1 way for them to sit on those chair, the chairs for B and E can be selected in 6C2 ways = 15

Now remaining 4 chairs can be occupied by other 4 people in 4! ways = 24 ways

Total ways : 6C2 x 4! = 15 x 24 = 360

Answer: Option D

**"GMATinsight"**Bhoopendra Singh & Sushma Jha

**Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions**

Whatsapp/Mobile: +91-9999687183 l [email protected]

Contact for

**One-on-One FREE ONLINE DEMO Class**Call/e-mail

**Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour**