Advanced Permutations and Combinations Problem

In summary, the problem asks for the number of points of intersection between the n given points when they are joined by straight lines in all possible ways, with the conditions that no two lines are parallel and no three lines meet at a point. The solution involves selecting pairs of the initial n points in nC2 ways and then subtracting the combinations that do not meet the given conditions.
  • #1
zorro
1,384
0

Homework Statement



There are n points in a plane which are joined in all possible ways by indefinite straight lines, and no two of these joining lines are parallel and no three of them meet in a point. Find the number of points of intersection, exclusive of the n given points.


The Attempt at a Solution



We can form straight lines with atleast 2 points.
So 2 points can be selected in nC2 ways.

Thats all I can understand.
Please help.
 
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  • #2
Given that you can select a pair of the initial [tex]n[/tex] points in [tex]\binom{n}{2}[/tex] ways, how many lines do you get? What do the conditions of the problem tell you about the number of points of intersection between anyone of these lines and another?
 
  • #3
This is the condition given-
'no two of these joining lines are parallel and no three of them meet in a point'
We have to formulate this in some combination and then subtract it from nC2.
 

FAQ: Advanced Permutations and Combinations Problem

What is the difference between a permutation and a combination?

A permutation is an arrangement of objects in a specific order, while a combination is a selection of objects without regard to order.

How do I know when to use permutations and when to use combinations?

Permutations are used when the order of objects is important, such as in a password or lock combination. Combinations are used when the order does not matter, such as in a lottery drawing or choosing a group of friends to go on a trip.

How do I calculate the number of possible permutations or combinations?

The number of permutations can be calculated using the formula n! / (n-r)!, where n is the total number of objects and r is the number of objects being arranged. The number of combinations can be calculated using the formula n! / (r!(n-r)!), where n is the total number of objects and r is the number of objects being selected.

Are there any shortcuts or tricks for solving advanced permutation and combination problems?

Yes, there are several techniques, such as using factorials, combinations with repetition, and the binomial theorem, that can help in solving complex permutation and combination problems. It is important to understand the principles behind these techniques in order to apply them correctly.

How can I apply permutations and combinations in real-life situations?

Permutations and combinations are used in many fields, including mathematics, statistics, computer science, and engineering. They can be used to solve problems involving probability, counting, and optimization. Some examples of real-life applications include creating unique passwords, organizing schedules, and designing experiments.

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