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

• Avi1995
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.
Avi1995
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. 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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