Can somebody help me with principles of counting questions?

[suskieanna]

I did similar stuffs before in maths methods but I still don't get this sort of question. Can somebody explain me how to solve these kind of questions?

- each of the 10 boys at a party shakes hands with each of the 12 girls. How many handshakes take place?

- How many ways can you make change for 50 cents using 5, 10 and 20 cent pieces?

- how many ways can six students be allocated to eight vacant desks?

- show that n! = (n^2-n) x (n-2)! for n greater or equal to 2.

Thank you

[TrueTears]

For your first three questions, I suggest having a read of the Art and Craft of Problem Solving by P. Zeitz, Chapter 6, if you are struggling to understand the intuition. For your last question, a simple induction argument works. Clearly true for , assume true for that is , now and we are done.