Choosing toppings for pizza Problem: Ordering a "deluxe" pizza means you have four choices from 15 available toppings. How many combinations are possible if toppings cannot be repeated? If they can be repeated? Assume the order in which the toppings are selected does not matter.
If the toppings cannot be repeated, then we have $C_4^{15}$ choices.
I am having difficulty with the toppings can be repeated problem.  It feels like this isn't solvable with the stars and bars method because we only care about "4" of the "15" toppings and not all 15.
What I think: Use "14" bars to then have "15" categories, each responding to a possible topping.  Have 4 stars to represent choosing a topping from that category.  Then we should get $C^{18}_{4}$?

You are correct if the toppings cannot be repeated.  If they can, presumably order does not matter, but you need to specify if which one is repeated does.  Is AABC different from ABBC because in the first case you get twice as much A as C?  
Assuming it matters which are repeated, you can have four different toppings, two of one and one each of two others, three of one and one other, or ... For two of one and one each of two others you have $15$ choices for the repeated one and $14 \choose 2$ for the others.  Do this for each pattern and you are done.
