A boat crew consist of 8 men, 3 of whom can row only on one side and 2
only on the other. The number of ways in which the crew can be
arranged is
This is a problem my math teacher has given to us as an exercise. Answer given is $1728$. We were asked to derive the answer. I could understand how the answer is $1728$. The following explanation is taken from beatthegmat.com
You can arrange each side using 4! But you have 3 guys that are
flexible and can sub anywhere. So 3*4!*4!
careerbless.com also derives the answer $1728$. But, they also explains answer can be $8$ if the question is interpreted as follows
(1) there is no restriction on how many people can sit on a side.
(2) arrangements of the persons within a particular side does not
matter.
So, I ended up with the following doubts
(1) Whether the most obvious answer is $8$ or $1728$ for this question?
(2) If assumptions are made as careerbless team did, then, I can come
up with my own assumptions as well. For example, If I read this
question as(1) there is no restriction on how many people can sit on a side.
(2) arrangements of the persons within a particular side are important
In this case, I may get another answer as 8×4!×4!
As a student, It is important for me to clear this as all problems can also be read in similar manner. Please help to clear my doubts as it is impossible for me to get such a support in classroom.
Best Answer
I see why you're unsure how to proceed. There are unstated assumptions in the question. In an ideal world, you'd know exactly what's being asked, but this isn't an ideal world.
I can tell you why I'd suspect that there need to be four rowers on each side, though: