Sum multiple probabilities

Hi there,

My problem is;
I have a number of cards in a deck (x), with a value between 0 and 7. There may be any number of each value (e.g. 3 cards worth 7, 10 worth 2 etc)
I draw 4 cards.

I want to know what the probability is of my total hand value being 0, 1, 2, 3, 4 ...... 28 to be able to then plot it on a graph.

I started off approaching it by;
x= total cards in deck
y= number of cards worth 0
z= number of cards worth 1

Probability of total value of 0 =COMBIN(y,4)/COMBIN(x,4)


However the combinations to get a total hand value of anything beyond 2 or 3 end up becoming huge.

Any help would be greatly appreciated!