So how many pickup combination are there on a Comanche VI? One answer is obtained by computing all the different settings of the switches: 2 x 2 x 2 = 8 combinations on the pickup switches and 3 x 3 x 3 = 27 combinations for the coil selectors, for a total of 8 x 27 = 216 combinations. However, this would be incorrect! To compute the number of sounds one can produce, more care has to be applied. There are 3 ways to use a single pickup, each with 3 coil combinations. This contributes 3 x (3) = 9 to the total. There are 3 distinct ways to select 2 pickups out of the 3: neck & middle, neck & bridge, and middle & bridge. Since each pickup has 3 settings, we have 3 x (3 x 3) = 27 combinations with 2 pickups engaged. Finally, there is only 1 combination with all 3 engaged, contributing another 1 x (3 x 3 x 3) = 27 combinations. So the total is 9 (for 1 pickup) + 27 (for 2 pickups) + 27 (for 3 pickups) = 63 combinations. QED.

Note that this result can also be obtained much easier. Instead of the existing 6 switches, imagine 3 4-position toggle switches, off/lower half-coil/both half-coils/upper half-coil, providing identical functionality. This results in (4 x 4 x 4) = 64 switch combinations. However, the off-off-off combination is useless, leaving one with the same 63 combinations as above.