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A Combinatorics Problem

  • Thread starter Avi1995
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  • #1
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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.
34nqfqt.jpg

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.
 

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tiny-tim
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