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7th grade

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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 - ,

    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 - ,

    How did you figure out the 30 and what does the c stand for?

  • 7th grade - ,

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

  • 7th grade - ,

    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 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

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