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algebra

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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 -

    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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