- #1

Avi1995

- 21

- 0

**Ques: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,in how ways can the crew be arranged?**

**Basic formulae of combinatorics(Permutations and combinations)**

**Well I do not have good knowledge of boats, but I used the following figure in this problem.**

1 will always be on stroke side,

Number of ways in which 2 people can be arranged in bow sides:2

The remaining 5 can be divided into groups of (5,0)(0,5),(4,1)(1,4),(3,2)(2,3) to row on each side,

Total ways are:

2*[2*(5C5)*5!+2*(5C4)*4!+2*(5C3)*3!*2!]

Multiplying all I get=480 way off the answer given in the book which 5760.

1 will always be on stroke side,

Number of ways in which 2 people can be arranged in bow sides:2

The remaining 5 can be divided into groups of (5,0)(0,5),(4,1)(1,4),(3,2)(2,3) to row on each side,

Total ways are:

2*[2*(5C5)*5!+2*(5C4)*4!+2*(5C3)*3!*2!]

Multiplying all I get=480 way off the answer given in the book which 5760.