How many possible sequences of tennis matches with 6 players over 4 weeks?

In summary, there are 15 possible pairs of players and 15P4 possible sequences of 4 matches. If one person is excluded, there are 5 possible pairs and (5C2)P4 possible sequences. The solution for excluding two players would require further exploration.
  • #1
JasonJo
429
2
There are 6 tennis players and each week for a month (4 weeks) a different pair of 5 play a tennis match. How many ways are there to form the sequence of 4 matches so that every player plays at least once?

I believe this is an OR problem, but I don't know how to handle the 4 weeks information and how do you count this?

thanks
 
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  • #2
The 4 weeks just refers to the 4 matches. Since there are 6 players there are 6C2 = 15 pairs. Now with 4 matches there are 15P4 possible sequences (since sequences means that the order matters). If we wanted to exclude one person we would have 5C2 pairs and (5C2)P4 possible sequences. What if we tried to exclude two people? Can you go from here?

-Dale
 

FAQ: How many possible sequences of tennis matches with 6 players over 4 weeks?

What is combinatorics and why is it important?

Combinatorics is a branch of mathematics that deals with counting and arranging objects. It is important because it helps us solve problems involving combinations and permutations, which have real-world applications in fields such as computer science, economics, and genetics.

What are the basic principles of combinatorics?

The basic principles of combinatorics include the fundamental counting principle, permutations, combinations, and the inclusion-exclusion principle. These principles help us count and organize objects in various ways to solve combinatorial problems.

How do I approach solving a combinatorics problem?

The first step in solving a combinatorics problem is to clearly define the problem and identify the type of problem it is (e.g. counting, arrangement, selection). Then, use the appropriate combinatorial principle or formula to solve the problem, and finally, check your answer to ensure it makes logical sense.

What is the difference between a combination and a permutation?

A combination is a selection of objects where the order does not matter, while a permutation is a selection of objects where the order does matter. For example, choosing a group of 3 people from a group of 10 can be a combination, as the order in which the people are chosen does not matter. However, arranging those 3 people in a line or sequence would be a permutation, as the order in which they are arranged does matter.

Are there any real-world applications of combinatorics?

Yes, combinatorics has many real-world applications. For example, it is used in coding theory to design error-correcting codes, in genetics to study and predict patterns of inheritance, and in economics to analyze decision-making and market behavior. Combinatorics is also used in computer science for algorithms and data structures, and in chemistry for molecular configuration and reactions.

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