Did you try generating functions?
Let be the number of non-negative solutions to,
.
Create the generating function,
.
Now, realize that,
Where,
Thus, by geometric series,
Does that work out?
So i know I need to use combinatorix for this, but I'm not exactly sure how.
4.3.19 In how many ways can you make change for a dollar, using pennies, nickels, dimes, quarters, and half-dollars? For example, 100 pennies is one way; 20 pennies, 2 nickels, and 7 dimes is another. Order doesn't matter.
Thanks in advance!