|
|
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.
15 Apr 2014, 03:15
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
58% (02:31) correct
42%
(02:47)
wrong
based on 347
sessions
History
Date
Time
Result
Not Attempted Yet
In a railway compartment, there are 2 rows of seats facing each other with accommodation for 5 in each, 4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated?
A.172000
B.12600
C.45920
D.43200
A.172000
B.12600
C.45920
D.43200
25 Oct 2015, 22:13
Kudos
Bookmarks
suryav
Here is another way to think about it - each seat is distinct. 5 face forward and 5 face back.
Start with the 4 people who want to face forward - for the first one, there are 5 options, for next one, 4 options and so on till we get 5*4*3*2.
Next, go on to 3 people who want to face back - for the first one, there are 5 options, for the next one, 4 options and so on till we get 5*4*3.
Now, we have 3 seats leftover and 3 indifferent people who can be arranged in 3*2*1 ways.
All in all, we can arrange 10 people in 5*4*3*2*5*4*3*3*2*1 = 14400 * 3 = 43200
Answer (D)
15 Apr 2014, 03:26
Kudos
Bookmarks
suryav
A --> E
B --> F
C --> G
D --> X
X --> X
The total number of arrangements = \(5!*5!*C^1_3=43,200\), where 5! is the number of ways to arrange 5 people facing forward, 5! is the number of ways to arrange 5 people facing backward, and \(C^1_3\) is the number of ways to choose 1 out of 3 indifferent who will face forward (the remaining 2 will face backward).
Answer: D.
