Randomness

Each morning when I arrive at the gym, I'm greeted by an unsually chipper undergrad who swipes my i.d. card and asks me if I need anything. She means a lock or a towel, but what I really need at that moment is a cup of coffee. On the counter next to her computer is a small whiteboard which features the Question of the Day. It's always a random trivia question, most of which I don't know.

Which state has the same number of cows as people?

What is the only food that never spoils?

When was the last time UNC-CH won the NCAA men's basketball tournament (before this year, of course)?

How many ways are there to make change for a dollar?

Being a math teacher, this last question intrigued me. I peeked at the answer (on the back of the whiteboard) and it said 293. Really? It seems that there would be more. Then I started trying to figure out how you would come up with the right answer without breaking out nickels, dimes, quarters, and pennies.

I'm thinking I should be able to figure this out- it's a combination, not a permutation, right? Is it a basic counting principle problem? This is making my head hurt.