How can a rowing crew be arranged with specific roles for each member?

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SUMMARY

The arrangement of an eight-man rowing crew with specific roles can be calculated using combinatorial principles. In this scenario, 2 oarsmen can only row on the bow side, and 1 can only row on the stroke side. The total number of arrangements is derived from the formula: 2*[2*(5C5)*5! + 2*(5C4)*4! + 2*(5C3)*3!*2!], resulting in 480 arrangements, which contradicts the book's answer of 5760. The discrepancy highlights the importance of accurately applying combinatorial formulas in rowing crew arrangements.

PREREQUISITES
  • Understanding of basic combinatorial principles, specifically permutations and combinations.
  • Familiarity with the structure of a rowing crew, including roles and side assignments.
  • Knowledge of binomial coefficients, denoted as "nCk".
  • Ability to perform factorial calculations, denoted as "n!".
NEXT STEPS
  • Study advanced combinatorial techniques, focusing on arrangements with restrictions.
  • Learn about the application of binomial coefficients in real-world scenarios.
  • Explore the principles of team dynamics in sports, particularly in rowing.
  • Investigate common errors in combinatorial problem-solving and how to avoid them.
USEFUL FOR

This discussion is beneficial for mathematicians, sports coaches, and team managers involved in rowing, as well as students studying combinatorial mathematics.

Avi1995
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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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