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## Homework Statement

To put it simply, there are 4 different flavors of ice cream, and 6 different toppings.

a)how many sundaes are possible using one flavor of ice cream and 3 diff toppings?

b)How many sundaes are possible using one flavour of ice cream and from 0 to 6 toppings?

c)How many different combinations of flavors of 3 scoops of ice cream are possible if it is permissible to make all 3 scoops the same flavor?

## Homework Equations

nCr

## The Attempt at a Solution

a)4*(4C3) = 80

b)4*(4C0)+4*(4C1) etc up until 6.. I get a 256.

c) This is the part I'm not so sure at...

For each scoop, there are 256 combinations.. so therefore we look at it from the perspective of the different combinations of whether the scoops are of the same flavor or not? like

SSS, SDD, DDD, SSD, same and different

so 256x3! ?