Arranging a rowing crew

An eight‑man boat has four bow seats and four stroke seats. Two men can row only on the bow side, one man can row only on the stroke side, and the remaining five men can row on either side. In how many ways can the crew be arranged?

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XI. Permutations and Combinations, Examples XI.a, No. 27