|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
05 Mar 2021, 03:45
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
49% (02:26) correct
51%
(02:36)
wrong
based on 79
sessions
History
Date
Time
Result
Not Attempted Yet
Six people A, B, C, D, E, and F are to arranged in a in a row. What is the probability that there are at least three people between A and B?
A. 1/15
B. 1/5
C. 1/3
D. 1/2
E. 2/3
A. 1/15
B. 1/5
C. 1/3
D. 1/2
E. 2/3
16 Mar 2021, 06:53
Kudos
Bookmarks
Bunuel
When there are 3 people between A and B
1*4*3*2 *1 *2*2 =96
1= Position of A
4*3*2= after arranging A and B the remaining 4 people can be arranged in 4*3*2 ways in between for the 3 spots.
1= Position of B fixed
2= Position of A and B can be interchanged, hence A and B can be positioned in two ways
2= The last person can go either to the left of A or to the right of B , hence he has two ways.
When there are four people in between A and B :
1*4*3*2*1*1*2 =48
1= Position of A
4*3*2*1= The remaining 4 people can be arranged in the 4 spots in between.
1= Position of B
2= Position of A and B can be interchanged, hence A and B can be positioned in two ways
So total ways at least 3 people are in between = 96 +48 = 144
Total ways 6 people can be arranged in a row without any restrictions = 6! = 720
Probability =\( \frac{144}{720}= \frac{1}{5}\)
Bunuel can you please check the options or Please can you provide the OE.
Thank you.
