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A Combinatorics Problem

  1. Apr 19, 2012 #1
    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.
     
  2. jcsd
  3. Apr 19, 2012 #2

    tiny-tim

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