algebra
posted by Matt .
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?

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 2^71 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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