2009 Mathematics Extension 1 Binomial Question Help please!! (1 Viewer)

[smile12]

If anyone can give me help with question 6b) that would be great! (I got the first part of i) - the sum part- and (1) in ii) but I don't know where to start with the rest and the BOS answers won't load on my computer.

http://www.boardofstudies.nsw.edu.a...doc/2009-hsc-exam-mathematics-extension-1.pdf

 

[Carrotsticks]

If we take the first diagonal, there are 2 possible points, and we need 2 to make an interval. So 2C2.

The second one has 3 possible points, but we need 2 to make an interval. So 3C2

So on and so forth until you reach the 'longest' diagonal, which is exactly the diagonal of the square, which has n points. Similarly, nC2.

And if we keep going further, the number decreases again, kind of like a pyramid.