1. ## 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

2. $\displaystyle K_1$ 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....

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