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)