We need to understand that it takes two points to determine a straight line. So the problem can be transformed into: how many combinations of two points are selected from five points, and the problem is solved by permutation and combination.
The combination formula in combinatorial mathematics tells us that the number of ways in which any k elements are combined by n different elements is: C(n, k)=n/(k*(n-k)), where! Represents factorial.
In this case, n=5(5 points) and k=2 (2 points need to be selected to determine a straight line). So, we need to calculate c (5 5,2).
C(5，2)=5/(2*(5-2)).
Calculated, c (5 5,2) =10.
So from these five points, at most 10 straight lines can be determined. This 10 straight line is determined by any two of these five points.
Advantages of permutation and combination:
1, flexibility: permutation and combination allow us to deal with various situations and problems, from simple counting problems to complex probability analysis, which can be solved by permutation and combination.
2. Intuitiveness: The concept of permutation and combination is intuitive and easy to understand. Even when dealing with complex problems, we can understand and solve them in an intuitive way.
3. Universality: permutation and combination are widely used in many fields, including mathematics, physics, engineering and computer science.
4. Systematization: permutation and combination have a complete theoretical system, including permutation number, combination number and Yang Hui triangle, which enables us to solve various problems systematically.
5. Developability: permutation and combination can be continuously developed and improved with the deepening of research, so as to better adapt to new application requirements.
6. Cultivate thinking: Learning permutation and combination can not only help us solve specific problems, but also cultivate our logical thinking and abstract thinking ability.
7. Cultivate thinking: Learning permutation and combination can not only help us solve specific problems, but also cultivate our logical thinking and abstract thinking ability.