It is currently 19 May 2019, 00:21
My Tests

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.

Four pool balls—A, B, C, D—are randomly arranged in a straig

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Founder
Founder
User avatar
Joined: 18 Apr 2015
Posts: 6553
Followers: 105

Kudos [?]: 1248 [0], given: 5939

CAT Tests
Four pool balls—A, B, C, D—are randomly arranged in a straig [#permalink] New post 08 May 2019, 04:28
Expert's post
00:00

Question Stats:

33% (01:00) correct 66% (00:42) wrong based on 3 sessions
Four pool balls—A, B, C, D—are randomly arranged in a straight line. What is the probability that the order will actually be A, B, C, D ?

(A) \(\frac{1}{4}\)

(B) \(\frac{1}{4C_4}\)

(C) \(\frac{1}{4P_4}\)

(D) \(\frac{1}{2!}\)

(E) \(\frac{1}{3!}\)
[Reveal] Spoiler: OA

_________________

Get the 2 FREE GREPrepclub Tests

Intern
Intern
Joined: 03 Apr 2019
Posts: 9
Followers: 0

Kudos [?]: 8 [0], given: 1

Re: Four pool balls—A, B, C, D—are randomly arranged in a straig [#permalink] New post 12 May 2019, 20:14
Can someone please help me with this question?
Founder
Founder
User avatar
Joined: 18 Apr 2015
Posts: 6553
Followers: 105

Kudos [?]: 1248 [0], given: 5939

CAT Tests
Re: Four pool balls—A, B, C, D—are randomly arranged in a straig [#permalink] New post 13 May 2019, 02:18
Expert's post
A ball cannot exist in two slots, so repetition is not allowed.


Each ball is given a different identity A, B, C, and D, so there are no indistinguishable objects.

Here, n = 4 (number of balls to arrange) in r = 4 (positions). We know the problem type, and the formula to use. Hence, by Formula 2, the number of arrangements possible is \(4P_4\) , and {A, B, C, D} is just one of the arrangements. Hence, the probability is 1 in \(4P_4\) , or \(\frac{1}{4P_4}\).

The answer is (C).
_________________

Get the 2 FREE GREPrepclub Tests

1 KUDOS received
Intern
Intern
User avatar
Affiliations: Partner at MyGuru LLC.
Joined: 13 May 2019
Posts: 36
Location: United States
GMAT 1: 770 Q51 V44
GRE 1: Q169 V168
WE: Education (Education)
Followers: 0

Kudos [?]: 24 [1] , given: 0

CAT Tests
Re: Four pool balls—A, B, C, D—are randomly arranged in a straig [#permalink] New post 13 May 2019, 07:09
1
This post received
KUDOS
An easy mnemonic way to distinguish between Permutations and Combinations is that a Permutation is a permanent unique iteration where order matters, such as this situation where A | B | C | D is not the same outcome as C |B | D | A. Whereas, a Combination is an iteration where order does not matter and can be changed for instance if we were to select four candidates for two identical job openings this would be a combination since it would not matter whether a person were selected for opening one or two.

As it pertains to this specific question, we should be able to conceptually determine that there is only one method for selecting exactly A | B | C | D as requested. Then, we can determine that there would be four ways to select the first ball, three for the second ball, two for the third ball, and only one for the fourth ball. Since we are selecting each of those four balls, it is necessary to multiply each of the possible outcomes together to determine the total number of possibilities. Therefore, there would be 4 x 3 x 2 x 1 or 4! = 16 total possibilities and we are exactly seeking one of those choices, so you may be able to determine that the correct answer should be 1/16. However, of course neither 1/16 nor 1/4! are available options, so we just recall our mnemonic to determine that this scenario is a Permutation that would be permanently set without the flexibility to change spots to inform that we would need to select the P formula in choice C rather than the C formula in choice B.
Re: Four pool balls—A, B, C, D—are randomly arranged in a straig   [#permalink] 13 May 2019, 07:09
Display posts from previous: Sort by

Four pool balls—A, B, C, D—are randomly arranged in a straig

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.