Use simple, concrete examples to motivate "n choose k".
Then ask what 5 choose 2 is and if there's a way to compute n choose 2 in general.
Then use 5 choose 3 as an example of the attempt to find n choose 3.
5 choose 3 apparently is equal to 5 choose 2. Why is that? Is it just "by accident"?
Discover that n choose k = n choose (n-k).
And perhaps find a formula for n choose 3.
Then ask what about a formula for n choose k in general?
Sam and I have started to write this out: A discussion about lunch possibilities
NOTE: This is also related to the workshop about (a+b)^n.