Question

An eight-oared boat is to be manned by a crew chosen from $11$ men, of whom $3$ can steer but cannot row, and the rest can row but cannot steer. In how many ways can the crew be arranged, if two of the men an only row on bow side?

Answer 1

Number of ways of arranging $8$ men who can row out of $8$ men $={}^8{P}_8=8!\text{ways.}$

Number of ways of arranging $2$ men who can steer out of $3$ men $={}^3{P}_2=3!=6\text{ways.}$

Hence, total number of arrangements of crew $=8!\times 6\text{ways.}$