NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 15:13 It is currently 26 Apr 2024, 15:13
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

The vertices of a regular pentagon are to be colored using five differ

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10161
Own Kudos [?]: 16600 [22]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
The vertices of a regular pentagon are to be colored using five differ [#permalink] New post   05 Jul 2019, 00:52
2
Kudos
20
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

63% (01:54) correct 37% (02:14) wrong based on 185 sessions
Hide Show timer Statistics
[GMAT math practice question]

The vertices of a regular pentagon are to be colored using five different colors. In how many ways can the pentagon’s vertices be colored if the 5 colors are to be chosen from a palette of 6 different colors?

A. 64
B. 96
C. 108
D. 144
E. 192
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
P
rxb266
Manager
Manager
Joined: 30 Nov 2018
Posts: 202
Own Kudos [?]: 149 [9]
Given Kudos: 79
Location: India
Concentration: Strategy, Marketing
Schools: HEC MiM '21 HEC Sept'22 Intake ISB '24 Rotman '24
GPA: 4
Send PM
Re: The vertices of a regular pentagon are to be colored using five differ [#permalink] New post   05 Jul 2019, 01:54
6
Kudos
3
Bookmarks
Solution:
we can choose 5 colours from a total of 6 colours in 6C5 ways ie 6 ways !!
we can arrange these 5 chose colours in (5-1!) ways ( since the arrangement is similar to the circular arrangement)

thus total no. of ways: 6C5 x (5-1)! = 144 ways
General Discussion
User avatar
L
nick1816
Retired Moderator
Joined: 19 Oct 2018
Posts: 1878
Own Kudos [?]: 6296 [2]
Given Kudos: 704
Location: India
Send PM
Re: The vertices of a regular pentagon are to be colored using five differ [#permalink] New post   05 Jul 2019, 03:30
1
Kudos
1
Bookmarks
Number of ways to select 5 different colors out of 6 different colors= 6C5=6

Number of ways to arrange 5 different colors on the vertices of regular pentagon= 5!/5=24

Number of ways the pentagon’s vertices can be colored if the 5 colors are to be chosen from a palette of 6 different colors= 6*24= 144



MathRevolution wrote:
[GMAT math practice question]

The vertices of a regular pentagon are to be colored using five different colors. In how many ways can the pentagon’s vertices be colored if the 5 colors are to be chosen from a palette of 6 different colors?

A. 64
B. 96
C. 108
D. 144
E. 192
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5344
Own Kudos [?]: 3968 [1]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
Re: The vertices of a regular pentagon are to be colored using five differ [#permalink] New post   05 Jul 2019, 04:39
1
Bookmarks
MathRevolution wrote:
[GMAT math practice question]

The vertices of a regular pentagon are to be colored using five different colors. In how many ways can the pentagon’s vertices be colored if the 5 colors are to be chosen from a palette of 6 different colors?

A. 64
B. 96
C. 108
D. 144
E. 192


Total no of ways pentagon's vertices be colored = 6C5 * 4! = 6*24 = 144

IMO D
User avatar
D
philipssonicare
Senior Manager
Senior Manager
Joined: 15 Feb 2018
Posts: 424
Own Kudos [?]: 385 [0]
Given Kudos: 2380
Send PM
Re: The vertices of a regular pentagon are to be colored using five differ [#permalink] New post   07 Jul 2019, 17:46
Combinations/permutations type questions, unless extremely basic, are much harder than sub-600. No chance this is sub-600.
User avatar
L
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10161
Own Kudos [?]: 16600 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: The vertices of a regular pentagon are to be colored using five differ [#permalink] New post   07 Jul 2019, 18:26
Expert Reply
=>

The number of ways to choose \(5\) colors out of \(6\) colors is 6C5 = \(6\).

The number of circular permutations of the \(5\) colors is \((5-1)! = 4! = 24.\)

Thus, \(6*24 = 144\) different colorings of the pentagon are possible.

Therefore, D is the answer.
Answer: D
User avatar
P
prabsahi
Manager
Manager
Joined: 09 Jun 2014
Posts: 228
Own Kudos [?]: 280 [1]
Given Kudos: 205
Location: India
Concentration: General Management, Operations
Send PM
Reviews Badge
Re: The vertices of a regular pentagon are to be colored using five differ [#permalink] New post   07 Jul 2019, 19:09
1
Kudos
MathRevolution wrote:
=>

The number of ways to choose \(5\) colors out of \(6\) colors is 6C5 = \(6\).

The number of circular permutations of the \(5\) colors is \((5-1)! = 4! = 24.\)

Thus, \(6*24 = 144\) different colorings of the pentagon are possible.

Therefore, D is the answer.
Answer: D




Hello Mathsrevolution,

Can you please explain the highlighted part

The number of circular permutations of the \(5\) colors is \((5-1)! = 4! = 24.\)
User avatar
L
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10161
Own Kudos [?]: 16600 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: The vertices of a regular pentagon are to be colored using five differ [#permalink] New post   09 Jul 2019, 19:53
Expert Reply
prabsahi wrote:
MathRevolution wrote:
=>

The number of ways to choose \(5\) colors out of \(6\) colors is 6C5 = \(6\).

The number of circular permutations of the \(5\) colors is \((5-1)! = 4! = 24.\)

Thus, \(6*24 = 144\) different colorings of the pentagon are possible.

Therefore, D is the answer.
Answer: D



The number of ways to arrange n distinct objects along a fixed (i.e., cannot be picked up out of the plane and turned over) circle is (n-1)!.
The number is (n-1)! instead of the usual factorial n! since all circular permutations of objects are equivalent because the circle can be rotated.

Hello Mathsrevolution,

Can you please explain the highlighted part

The number of circular permutations of the \(5\) colors is \((5-1)! = 4! = 24.\)



The number of ways to arrange n distinct objects along a fixed (i.e., cannot be picked up out of the plane and turned over) circle is (n-1)!.
The number is (n-1)! instead of the usual factorial n! since all circular permutations of objects are equivalent because the circle can be rotated.
avatar
B
kheraarj
Intern
Intern
Joined: 07 Dec 2018
Posts: 6
Own Kudos [?]: 1 [0]
Given Kudos: 199
Location: India
Schools: Queen's Jan20 Intake Ivey '21 HEC Montreal '21
Send PM
Re: The vertices of a regular pentagon are to be colored using five differ [#permalink] New post   19 Jul 2019, 13:18
How do we know that the order of color doesnot matter in this case?

Suppose that we have green, red, blue, yellow, brown, black-- 6 colors

We can have blue first, then an option of any of the 5 colors in the second wall, then any 1 of the 4 in the 3rd, then any of 3 in the 4th, and then any of the 2 in the 5th.

There are 6 ways to do the same (for each color), therefore answer should be 6!

Why is the above wrong?

Posted from my mobile device
User avatar
S
Stanindaw
Manager
Manager
Joined: 11 Dec 2020
Posts: 135
Own Kudos [?]: 46 [0]
Given Kudos: 55
Location: United States (NY)
Concentration: Operations, Economics
Schools: Booth '26
GPA: 3.7
Send PM
Reviews Badge
Re: The vertices of a regular pentagon are to be colored using five differ [#permalink] New post   04 Dec 2022, 02:58
MathRevolution wrote:
[GMAT math practice question]

The vertices of a regular pentagon are to be colored using five different colors. In how many ways can the pentagon’s vertices be colored if the 5 colors are to be chosen from a palette of 6 different colors?

A. 64
B. 96
C. 108
D. 144
E. 192

Will we use (n-1)! for triangle too??
GMAT Club Bot
gmatclubot
Re: The vertices of a regular pentagon are to be colored using five differ [#permalink]
04 Dec 2022, 02:58
Moderators:
Bunuel
Math Expert
92948 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions