Solving Subset Sum Counting: How to Make £2 from Coins

[martix]

Homework Statement

How many different ways can £2 be made using any number of coins?
(In other words, how many ways can you obtain the sum of 200 with terms from the following finite set - 200, 100, 50, 20, 10, 5, 2, 1. Order does not matter.)

Homework Equations

None?

The Attempt at a Solution

No idea.
I've been mulling over this problem for way too much time now without producing anything viable.
A PnP solution is beyond me at this point. On the computational side I've been thinking of a recursive solution which should spawn this massive recursion tree and I'm pretty sure there's got to be a better method out there.

 

[micromass]

Do you know generating functions??

 

[martix]

Nope...
First time I've heard of those. I can always read up on them if they are relevant to the solution.