Posted by **Alexia** on Monday, January 4, 2010 at 9:05pm.

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**, Monday, January 4, 2010 at 9:28pm
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**, Monday, January 4, 2010 at 9:40pm
How did you figure out the 30 and what does the c stand for?

- 7th grade -
**Alexia**, Monday, January 4, 2010 at 9:41pm
Also what is the (5,3); I didn't learn that yet.

- 7th grade -
**Reiny**, Monday, January 4, 2010 at 10:04pm
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??

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