|
|
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.
28 Sep 2018, 09:56
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
32% (02:14) correct
68%
(02:04)
wrong
based on 151
sessions
History
Date
Time
Result
Not Attempted Yet
During a war a Major is supposed to send 5 units of soldiers to 5 different borders. If he has 30 soldiers and has to send an equal number of soldiers to 5 regions, in how many ways can he do so?
A. \(30!/(5!)^6\)
B. \(30!/(5!)^5\)
C. \(30!/(6!)^5\)
D. \((30!/6!^5)5!\)
E. \(30!/(6!^5*5!)\)
A. \(30!/(5!)^6\)
B. \(30!/(5!)^5\)
C. \(30!/(6!)^5\)
D. \((30!/6!^5)5!\)
E. \(30!/(6!^5*5!)\)
28 Sep 2018, 10:50
Kudos
Bookmarks
a70
Straight formula ..
If you have to make 5 groups of 6 people from (5*6) people, answer is \(\frac{(5*6)!}{(6!)^5}\)
Now if you do not know the formula..
First 6 can be selected in 30C6
Next 6 from remaining 24 in 24C6 and so on
So 30C6*24C6*18C6*12C6*6C6
\(\frac{30!}{24!6!}*\frac{24!}{18!6!}*\frac{18!}{12!6!}*\frac{12!}{6!6!}*\frac{6!}{0!6!}=\frac{30!}{6!6!6!6!6!}=\frac{30!}{(6!)^5}\)
C
General Discussion
30 Sep 2018, 09:14
Kudos
Bookmarks
a70
Using the concept, if 2n different items are to divided into 2 groups of n items each, then it can be done in \(\frac{(2n)!}{{n!*n!*2!}}\)
Here we have 30 soldiers, hence 5*6 items to be divided into 5 groups of 6 items each.
30 soldiers can be divided into 5 units of 6 soldiers each in \(\frac{30!}{((6!)^{5}*5!)}\)
The 5 units can then be sent to the 5 different borders in 5! ways.
Hence total # of ways of doing this is = \(\frac{30!}{((6!)^{5}*5!)}*5!\) = \(30!/(6!)^5\)
Answer C.
Thanks,
GyM
