Square Scoops

Square Scoops
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Knowing about combinations and permutations can come in handy. Let's say you go to www.barbie.com and decide you want to design your own Barbie! How many different Barbies could be made? There are 4 faces colors, 3 eye colors, 3 lip colors, 4 hairstyles, and 6 hair colors. You have several ways to solve this problem. One way is to make all the different Barbies. Another is to draw them all out. The mathematical approach is to multiply 4 x 3 x 3 x 4 x 6. Hmmm, which way should you use?

The permutations you used on the card used three tiles taken three at a time. What if there were four flavors and you wanted to know how many ways you could make a two scoop cone with different flavors? Try building all the choices with color tiles before going on.

The mathematical solution is not very hard if you think about it. First, how many choices do you have for the first scoop? Four, right? Now there are three flavors left to choose. So very every first scoop, there are three possibilities for the second scoop. That means there are 4 x 3 or 12 possible cones.

What if you wanted to know how many triple cones can be make with four flavors? First scoop? Four choices. Second scoop? Three choices. Third scoop? Two choices. The total number is 4 x 3 x 2 or 24 choices.

But what about combinations? What if instead of getting a cone, we got a dish of ice cream!! Now the order doesn't matter. If we had 4 flavors and wanted to have a double dish, vanilla and chocolate would be the same as chocolate and vanilla.

Let's think about four color tiles taken two at a time. We know there are 12 possible permutations:
RG, RB, RY, GR, GB, GY, BR, BG, BY, YR, YG, YB
but RG is the same as GR, RB is the same as BR, and RY is the same YR. How many others are the same?

The mathematics behind combinations may be a little too tricky for this website but here's something to think about. To find the number of combinations of r things taken n at a time, divide the number of permutations of r things taken n at a time by r factorial. [r factorial is r x (r-1) x (r-2) x ... x 1]. Yikes!! You may not be ready for this yet, but you will be soon!! Math Power!!!