Posted by Alexia on .
How many combinations can you make with 3 toppings?
Ice Cream: Vanilla/ Chocolate/ Strawberry/ Coffee
Toppings: Fudge/ Caramel/ Chocolate Sprinkles/ Rainbow Sprinkles/ Nuts

7th grade 
Reiny,
there are C(5,3) or 10 combinations to choose 3 toppings from 5
If your questions is, "How many different ice cream cones can you have with three toppings"?
then it would be 3 x C(5,3) or 30 
7th grade 
Alexia,
How did you figure out the 30 and what does the c stand for?

7th grade 
Alexia,
Also what is the (5,3); I didn't learn that yet.

7th grade 
Reiny,
Sorry Alexia, should have noticed the "7th grade"
Suppose we use F,C,S,R, and N for the different toppings.
Now we want to form groups of 3 where the order does not matter.
so
FCS
FCR
FCN
FSR
FSN
FRN
CSR
CSN
CRN
SRN
There are 10 of these. Can you think of any more?
Now to the icecream.
there are 3 flavours, so each of the above 10 can be put on 3 different flavours, which give me 3x10 or 30
The notation C(5,3) you will learn in highschool, the C stands for Combinations, and the 5,3 means "choose 3 from 5"
For some extra "fun" you might look up Pascal's triangle, where numbers are arranged in the following pattern
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
the first column is all 1's
the second column is the counting numbers.
A new number is found by adding the one directly above and the one to the left of that
e.g. the 10 came from the 6 above it + the 4 to the left of the 6
Neat??