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
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
How did you figure out the 30 and what does the c stand for?
Also what is the (5,3); I didn't learn that yet.
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.
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 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