NEW HERE? LEARN MORE
closeclose
Last visit was: 01 May 2024, 23:56 It is currently 01 May 2024, 23:56
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 numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are to be arranged around

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92987
Own Kudos [?]: 620622 [9]
Given Kudos: 81712
Send PM
CAT Tests Forum Quiz Mode
The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are to be arranged around [#permalink] New post   07 Apr 2022, 05:45
9
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

62% (01:56) correct 38% (02:20) wrong based on 73 sessions
Hide Show timer Statistics
The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are to be arranged around a circle. What is the probability that the numbers 4,5,6 are together ?

A. 1/9!
B. 1/126
C. 5/126
D. 1/12
E. 2/9
ShowHide Answer
Official Answer
D
User avatar
B
Keerthanna
Intern
Intern
Joined: 10 Jan 2022
Posts: 20
Own Kudos [?]: 5 [2]
Given Kudos: 373
GMAT 1: 680 Q44 V39
GMAT 2: 710 Q47 V41
Send PM
Re: The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are to be arranged around [#permalink] New post   10 Apr 2022, 07:12
2
Bookmarks
Number of elements = 10

Number of arrangements in a circle = (n-1)! = (10-1)! = 9!

Now consider 4,5,6 as one entity -> number of elements = 8 => Number of arrangements = (8-1)! = 7!

Possible arrangements of 4,5,6 = 3!


Probability of 4,5,6 together = 7!*3!/9! = 3*2/9*8 = 1/12 B
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92987
Own Kudos [?]: 620622 [0]
Given Kudos: 81712
Send PM
CAT Tests Forum Quiz Mode
Re: The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are to be arranged around [#permalink] New post   01 May 2022, 03:23
Expert Reply
Bunuel wrote:
The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are to be arranged around a circle. What is the probability that the numbers 4,5,6 are together ?

A. 1/9!
B. 1/126
C. 5/126
D. 1/12
E. 2/9

___________________________
Anyone else want to try this one?
User avatar
L
PyjamaScientist
Admitted - Which School Forum Moderator
Joined: 25 Oct 2020
Posts: 1130
Own Kudos [?]: 1048 [0]
Given Kudos: 630
Schools: Ross '25 (M$)
GMAT 1: 740 Q49 V42 (Online)
Send PM
Reviews Badge
The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are to be arranged around [#permalink] New post   01 May 2022, 03:37
In how many ways can we place \(10\) digits in a circle?
\((10 - 1)!\) ways = total no. of ways.

For, \(4,5,6\) to always be together, we can consider them one single unit shuffling within themselves in \( 3!\) ways. Thus, now we have \(8\) entities,\( 7\) single digits and one consortium of \(4,5\) and \(6 \) behaving as a single unit. In how many ways can we arrange these \(8\) entities in a circle?
\((8-1)!\) ways.

So, the probability that the \(4,5\) and \(6\) always stay together \(= \frac{favourable outcomes}{total outcomes} = \frac{7!*3!}{9!} = \frac{1}{12}\) (D)
GMAT Club Bot
gmatclubot
The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are to be arranged around [#permalink]
01 May 2022, 03:37
Moderators:
Bunuel
Math Expert
92987 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