Question

Laura wants 3 scoops of ice cream. She can choose from vanilla, chocolate, mint, raspberry, blueberry, and coffee flavors.
How many combinations of 3 scoops of ice cream can Laura choose from? and is this a scenario in which repetition is allowed?

Answer 1

Case 1: she picks 3 different flavours, does not care in which order they are picked,
= C(6,3) = 20
(you could actually list those)

Case 2: repetition is allowed, order does not matter, e.g. {mint,mint,vanilla} or {ras,ras,ras}
triples: choose one of the 6 colours, C(6,1) = 6

double and single: choose the double flavour ---> 6
leaving 5 to choose for the single flavour
total of that case =30

total = 20 + 30 + 6 = 56

Now if we also cared in which order the flavours are put in the cone, it would change the argument.