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

In summary, there are 480 ways to arrange a crew of eight men on a boat, with two men on the bow side and one man on the stroke side. This is calculated using a basic formula of combinatorics, considering the different combinations of oarsmen on each side. This is a lower number than the answer given in the book, which is 5760.
  • #1
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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  • #2

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

1. What is combinatorics?

Combinatorics is a branch of mathematics that deals with counting and arranging objects in a systematic way.

2. What is a combinatorics problem?

A combinatorics problem is a mathematical problem that involves counting or arranging objects in a specific way.

3. What are some common types of combinatorics problems?

Some common types of combinatorics problems include permutations, combinations, and the binomial theorem.

4. How do you approach solving a combinatorics problem?

The first step in solving a combinatorics problem is to clearly define the problem and identify what you are trying to count or arrange. Then, use mathematical formulas and techniques to find the solution.

5. What are some real-life applications of combinatorics?

Combinatorics has many real-life applications, such as in computer science, statistics, and economics. It is used to solve problems related to data analysis, optimization, and decision making.

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