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kikar
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Could you give the exact wording of the question or rephrase it? I am unsure if you mean one quarter of all subsets of integers 1,2,3...m with three elements or not.
1> How many arrangements are there such that no two A's are beside each other?
shouldn't be a problem ... straightforward (only thing to remember ... 3 points cannot be collinear)
how many 3-subsets can you form? (call this A)
How many 3-subsets can contain integer 5? (call this B)
1/4 * A = B ... solve for m
4> no three segments cross at any point ...
therefore atmost two segments can cross each other ...
and every crossing of two segments produces 1 intersection point ...
so ??
you can arrange this in 13! ways because that's how many total letters there are?A .. First arrange the B's and y's? in how many ways can u do this?
Look at what i gave in the brackets ... can u see how to pick the points then?
got this thanksCan u find A and B? (atleast A is pretty simple)
Combinatorics is a branch of mathematics that deals with counting, arrangements, and combinations of objects or events.
Combinatorics has various applications in fields such as computer science, engineering, and economics. Some examples include analyzing algorithms, designing networks, and predicting stock market trends.
The most common approach to solving a combinatorics problem is by using counting techniques such as permutations, combinations, and the multiplication principle. It is also important to carefully read the problem and understand the given conditions before attempting to solve it.
Permutations refer to the number of ways to arrange a set of objects in a specific order, while combinations refer to the number of ways to select a subset of objects without considering their order.
The best way to improve your combinatorics skills is by practicing regularly and familiarizing yourself with various counting techniques. It is also helpful to read books, take online courses, and solve challenging combinatorics problems. Collaborating with other mathematicians or joining a combinatorics study group can also be beneficial.