In how many ways can the crew of a ten oared boat be arranged,when of

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!