Recurrence relation - "order matters" clause

Question

I'm having a bit of trouble understanding the order matters clause of a recurrence relation problem.

EX: A bus driver must pay a toll of 45 cents. Find a recurrence relation for the number of ways the driver can pay n cents. He can use only nickels and dimes.

My question: If the driver is trying to pay 10 cents, does that mean there are--

Three ways of paying: (first nickel + second nickel, second nickel + first nickel, dime)

OR

Two ways of paying: (two nickels, one dime)

Answer 1

If the question says somewhere that order matters I would read this as saying that the order in which you pay coins matters, but coins of the same type are indistinguishable from each other.

So 2 for your case. But for 15 cents the answer would be 3 because these are distinct: (nickel, nickel, nickel), (nickel, dime), and (dime, nickel).

However I would first look to see if there is an example matching my interpretation, and if not then I would ask the question of the teacher using 15 cents in the question.

Answer 2

It's not clear from the wording but most likely order does not matter since the same coins in any order will pay any given toll.