Please help me!! Probability! Need to turn this in soon, thank you!!

Question

The senior class of Serious Tech High School decided to have an ice cream party. They decide on ice cream cones. But being independent thinkers they each want to have a different cone. But the school will only provide three flavors of ice cream: vanilla, chocolate and strawberry. They know if they only do one scoop cones, they will only get three different cones. The students then figured out how many different cones they could make if they made double scoop cones.  

There are 80 students in the senior class of Serious Tech High School. How many scoops of ice cream would have to be used in each cone in order to make a different cone for each student in the senior class?

Answer 1

one scoop will get 3 students different cones

2 scoops will get 6 students: their cones SS, CC, VV, SV, VC, CS

3 scoops will get 10

4 scoops will get 15

5 will get 21

the pattern is 3,6,10,15, 21, 28, 36, 45, 55, 66, 78,91,...

11 scoops gets 78 students different cones

12 gets 91

You need at least 12 scoops per cone to have 80 student have all different cones

Answer 2

If the order of the scoops makes a difference:

4! = 24

5! = 120