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?

Answer 1

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.