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hanumath
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A boat is to be manned by eight men of whom two can only row on bow 01 Jan 2012, 19:10
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Difficulty:

85% (hard)

Question Stats:

42% (02:44) correct 58% (02:09) wrong based on 76 sessions

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A boat is to be manned by eight men of whom two can only row on bow side and one can only row on stroke side. In how many ways can the crew be arranged?

A. 4790
B. 4890
C. 5670
D. 5760
E. 5900
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D
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arvindravulavaru
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A boat is to be manned by eight men of whom two can only row on bow 01 Jan 2012, 22:30
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Hi Hanumath,

This is my first post too. :)
Please let me know, if this clarifies your doubt.

1. Taking 4 Men per Side
Bow Side: __ __ __ __
Row Side: __ __ __ __
2. Selection Process
3. Selecting 3 (2 on bow side and 1 on stroke side) - 1 way each
Bow Side: X X __ __
Row Side: X __ __ __
4. 5 left. Filling the 2 people from the bow side - C(5,2) [Remaining to the stoke side]
5. Arrange the Bow side in 4! ways and the Row side in 4! ways

Hence:
C(5,2)*4!*4! = 10*24*24 = 10*567 = 5670.

Thanks,
Arvind.
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hanumath
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A boat is to be manned by eight men of whom two can only row on bow 02 Jan 2012, 04:13
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Thanks a lot Arvind, this explanation definitely helps.

Cheers,
Hanumath
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KarishmaB
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A boat is to be manned by eight men of whom two can only row on bow Updated on: 08 Oct 2022, 03:33
Originally posted by KarishmaB on 03 Jan 2012, 03:39.
Last edited by KarishmaB on 08 Oct 2022, 03:33, edited 1 time in total.
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hanumath
Hi,

This is my first post and am glad to be here :-D . This forum certainly rocks.

Need some help in understanding and arriving at the solution for the below problem. Appreciate any help on this.

Q: A boat is to be manned by eight men of whom two can only row on bow side and one can only row on stroke side. In how many ways can the crew be arranged?

A) 5760

Thanks,
Hanumath.
Show more

Think of it this way:
We assume there are 4 men on the bow side and 4 on the stroke side (which, by the way, is not explicitly mentioned which is a failing of this question)
Of the 8 men, 2, say A and B, must be on the bow side.
1, say S, must be on the stroke side.

For A, there are 4 possible spaces (bow side places). For B, there are 3 possible spaces (one is already occupied by A). For S there are 4 possible spaces (on stroke side). For the fourth guy, there are 5 spots, for the fifth guy, there are 4 spots and so on...
Possible arrangements = 4*3*4*5*4*3*2*1 = 5760

This is what we call the basic counting principle.
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A boat is to be manned by eight men of whom two can only row on bow 09 Jan 2012, 15:00
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What is the source? The question is forcing me to make assumptions that are not valid in real GMAT.

For example, it is forcing me to assume 4 people on each side, which is the only way to arrive at the solution. I got the solution with this assumption, but not the "GMAT" way of solving the problem.
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A boat is to be manned by eight men of whom two can only row on bow 11 Jan 2012, 13:19
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(A1) (A2) (B1 B2 B3 B4 B5) (C1)

4!*2!*5!*1!=5760
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A boat is to be manned by eight men of whom two can only row on bow 28 Feb 2026, 05:40
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