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Math Help - Combinations

  1. #1
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    Combinations

    Ok say i have a bass guitar and want to figure out how many tone combinations i can have what is the equation and answer to this.
    There are 4 knobs, each knob has 3 positions, all knobs must be used at the same time and each knob can only use one position at a time
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  2. #2
    MHF Contributor
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    K_1 has 3 positions a, b, c

    K_2 has 3 positions d, e, f

    K_3 has 3 positions g, h, i

    K_4 has 3 positions j, k, l

    As each of the 4 knobs can be in any of the 3 positions,
    the position combinations are....

    adgj, adgk, adgl,
    adhj, adhk, adhl,
    adij, adik, adil,
    aegj, aegk, aegl,
    aehj, aehk, aehl,
    aeij, aeik, aeil,
    afgj, afgk, afgl,
    afhj, afhk, afhl,
    afij, afik, afil,

    and so on.
    Or.... first knob has 3 possible positions.
    For each of these 3, the second knob also can have 3 positions.
    The third one can be in any of 3 positions for each of the 2nd knob's positions. The 4th one can be in any of 3 positions for each of the 3rd one's 3 positions.

    This is 3(3)3(3)=3^4 combinations
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