
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

$\displaystyle K_1$ has 3 positions a, b, c
$\displaystyle K_2$ has 3 positions d, e, f
$\displaystyle K_3$ has 3 positions g, h, i
$\displaystyle K_4$ 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 $\displaystyle 3(3)3(3)=3^4$ combinations