1. Use a combinatorial argument to show that with
2. We are given points arranged around a circle and the chords connecting each pair of points are drawn. If no three chords meet in a point, how many points of intersection are there? For example, when there are intersections.
I just started combinatorics so please don't leave out any necessary steps! Thanks again
Q1: How many ways can we choose k things from m+n things? Split the m+n bunch into a group of m things and a group of n things. Then you could choose the k things by choosing 0 from the n group and k from the m group. Or you could choose 1 thing from the n group and k-1 from the m group.
Or you could choose 2 things from the n group and k-2 from the m group.
How many ways are there of doing these? That's your sum.
Q2. Any 4 points determine 1 intersection point. Think 2 intersecting chords from 4 points. So you've determined n choose 4 points.