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10 Jul 2019, 01:10
Kudos
Bookmarks
D
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:
34% (02:26) correct
66%
(02:05)
wrong
based on 111
sessions
History
Date
Time
Result
Not Attempted Yet
In how many ways can the crew of a ten oared boat be arranged, when of the ten persons available, 2 of whom can row only on the bow side and 3 of whom can row only on the stroke side?
A. \(\frac{10!}{2!*3!}\)
B. \(\frac{10!}{8!*7!}\)
C. \(\frac{5!}{3!*2!}\)
D. \(\frac{(5!)^3}{3!*2!}\)
E. \(\frac{5!}{8!*7!}\)
A. \(\frac{10!}{2!*3!}\)
B. \(\frac{10!}{8!*7!}\)
C. \(\frac{5!}{3!*2!}\)
D. \(\frac{(5!)^3}{3!*2!}\)
E. \(\frac{5!}{8!*7!}\)
10 Jul 2019, 03:52
Kudos
Bookmarks
Of the ten persons, 5 persons row on the bow side and 5 persons on the stroke side.
On the bow side, we already have 2 persons who only want to row on that side. Similarly, on the stroke side, we already have 3 persons who only want to row on that side.
This means, we are only left with 5 persons who do not have a preference towards rowing on a particular side. Of these 5 persons, any 2 can be selected to row on the stroke side. This will automatically ensure that the other 3 persons will row on the bow side.
Number of ways in which ANY 2 persons can be selected from 5 persons = \(5_C_2\) = \(\frac{5!}{(3! * 2!)}\).
Now, we need to take care of the arrangement part, since the question specifically asks about the number of ways in which the crew can be arranged.
On the bow side and the stroke side, the total number of arrangements possible is 5! and 5! respectively.
So, total number of ways of arranging the crew of 10 persons = \(\frac{5!}{(3! * 2!)}\) * 5! * 5! = \(\frac{(5!)^3}{(3!*2!)}\).
The correct answer option is D.
Hope this helps!
On the bow side, we already have 2 persons who only want to row on that side. Similarly, on the stroke side, we already have 3 persons who only want to row on that side.
This means, we are only left with 5 persons who do not have a preference towards rowing on a particular side. Of these 5 persons, any 2 can be selected to row on the stroke side. This will automatically ensure that the other 3 persons will row on the bow side.
Number of ways in which ANY 2 persons can be selected from 5 persons = \(5_C_2\) = \(\frac{5!}{(3! * 2!)}\).
Now, we need to take care of the arrangement part, since the question specifically asks about the number of ways in which the crew can be arranged.
On the bow side and the stroke side, the total number of arrangements possible is 5! and 5! respectively.
So, total number of ways of arranging the crew of 10 persons = \(\frac{5!}{(3! * 2!)}\) * 5! * 5! = \(\frac{(5!)^3}{(3!*2!)}\).
The correct answer option is D.
Hope this helps!
General Discussion
28 Jul 2019, 10:29
Kudos
Bookmarks
Bunuel
The two additional persons to row on the stroke side can be chosen in 5C2 = 5!/(3!*2!) ways. Notice that once this choice has been made, all the remaining crew must row on the bow side; therefore, there is only one way to choose the 5 people to row on the bow side.
The five people to row on the stroke side can be arranged in 5! ways. Similarly, the five people to row on the bow side can also be arranged in 5! ways. Therefore, the boat can be crewed in
5!/(3!*2!) * 5! * 5! = (5!)^3/(3!*2!)
ways.
Answer: D
