Hi amor_vincit_omnia,

a) Well assuming each flavour can go with each topping then we have tochooseone flavour out of 4 and thenchoose3 toppings out of 6. The order of the toppings do not matter and thus we can use combinations on the toppings. We are only interested in choosing one flavour and thus we can immediately say there are 4 ways of doing this without the need for cominations. Thus,

b) Now for each ice cream we can have either 0, 1, 3 etc. toppings. Well firstly just concentrate on the numbers of ways for one ice cream;

Thus the total numbers of ways for one ice cream is;

We have 4 ice creams so the total number of ways is