A boat is to be manned by eight men of whom 2 can only row on bow side and 1 can only row on stroke side, the number of ways in which the crew can be arranged is

Question

A boat is to be manned by eight men of whom 2 can only row on bow side and 1 can only row on stroke side, the number of ways in which the crew can be arranged is (A) 4360 (B) 5760 (C) 5930 (D) None of these

Tardigrade Admin · Accepted Answer

First we have to select 2 men for bow side and 3 for stroke side. The number of selections of the crew for two sides

=^{5} C_{2} \times^{3} C_{3}

For each selection there are 4 persons on both sides, who can be arranged in 4! × 4!ways.
Required number of arrangement

=^{5} C_{2} \times^{3} C_{3} \times 4! \times 4! = 5760

Q. A boat is to be manned by eight men of whom 2 can only row on bow side and 1 can only row on stroke side, the number of ways in which the crew can be arranged is

4360

5760

5930

None of these

First we have to select 2 men for bow side and 3 for stroke side. The number of selections of the crew for two sides =5C2​×3C3​ For each selection there are 4 persons on both sides, who can be arranged in 4! × 4!ways. Required number of arrangement =5C2​×3C3​×4!×4!=5760