It is currently 17 May 2024, 13:47
Register
GMAT Focus Tests
Decision Tracker
My Rewards
Unanswered
Active Topics
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

4 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Question banks

GMAT Question Banks

Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93333
CAT Tests Forum Quiz Mode
The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are to be arranged around [#permalink] The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are to be arranged around  07 Apr 2022, 05:45
9
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

61% (01:57) correct 39% (02:18) wrong based on 75 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
Official Answer and Stats are available only to registered users. Register/Login.

_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
B
Keerthanna
Intern
Intern
Joined: 10 Jan 2022
Posts: 20
GMAT 1: 680 Q44 V39
GMAT 2: 710 Q47 V41
Re: The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are to be arranged around [#permalink] The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are to be arranged around  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: 93333
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] The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are to be arranged around  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?
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
L
PyjamaScientist
Admitted - Which School Forum Moderator
Joined: 25 Oct 2020
Posts: 1130
Schools: Ross '25 (M$)
GMAT 1: 740 Q49 V42 (Online)
Reviews Badge
The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are to be arranged around [#permalink] The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are to be arranged around  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)
_________________
~vidyaya amrutam ashnute~
My Debrief: From 430 to 740.
Signature Read More
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
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
Bunuel
Math Expert
93332 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts