Posted by **Matt ** on Sunday, May 22, 2011 at 2:21pm.

A pack of Jillybeans contains seven different flavors: Apricot, Banana, Coconut, Date, Eggplant, Fig and Grape. You can make each flavor indivdually or come up with some crazy combinations. How many flavor combinations are possible with these seven flavors alone or mixed?

- algebra -
**MathMate**, Sunday, May 22, 2011 at 3:41pm
start with no flavour (which does not apply here), each time we add a flavour, we double the number of flavours.

So there are 2^7 flavour combinations for 7 flavours, *including* the no flavour at all "combination".

So there are 2^7-1 flavour combinations in total.

For example:

0 2^0 combination (no flavour at all, to be subtracted at the end)

A 2^1 combinations

B

AB 2^2 combinations

C

AC

BC

ABC 2^3 combinations

D

AD

BD

CD

ABD

ACD

BCD

ABCD 2^4 combinations

... etc.

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