Three gnomes and three elves sit down in a row of six chairs

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

Three gnomes and three elves sit down in a row of six chairs

by AAPL » Wed Jun 12, 2019 4:32 am

Timer

00:00

Your Answer

Global Stats

Manhattan Prep

Three gnomes and three elves sit down in a row of six chairs. If no gnome will sit next to another gnome and no elf will sit next to another elf, in how many different ways can the elves and gnomes sit?

A. 18
B. 36
C. 48
D. 72
E. 96

OA D

Quote

Source: Beat The GMAT — Problem Solving | Wed Jun 12, 2019 4:32 am

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 am; Location: Montreal; Thanked: 1090 times; Followed by:355 members; GMAT Score:780

by Ian Stewart » Wed Jun 12, 2019 5:59 am

If there's a gnome in the first chair, the arrangement must alternate: GEGEGE. We'll have 3 choices for the first gnome, 2 for the second, and 1 for the third, and the same for the elves, for 3! * 3! = 36 arrangements in total. But we can also have an elf in the first chair, and the arrangement could be EGEGEG, which will yield a further 36 arrangements. So we have 72 in total.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Jun 14, 2019 2:39 pm

AAPL wrote:Manhattan Prep

Three gnomes and three elves sit down in a row of six chairs. If no gnome will sit next to another gnome and no elf will sit next to another elf, in how many different ways can the elves and gnomes sit?

A. 18
B. 36
C. 48
D. 72
E. 96

OA D

We can see that one seating arrangement of gnomes (G) and elves (E) can be:

GEGEGE

The first G and E each has 3 choices; the second G and E each has 2 choices and the last G and E each has 1 choice. Thus the number of ways to have the "GEGEGE" seating arrangement is:

3 x 3 x 2 x 2 x 1 x 1 = 36

However, the seating arrangement can also be EGEGEG, and there will also be 36 such arrangements. Thus, the total number of seating arrangements is 36 + 36 = 72.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]