picture a pimply 17 year old, with no talent and a bunch of broken gear imitating a rocker. Then realizing he could jump around at bars for beer money.
ah! 
Oops…
9.9167793487094968920957140154189e+149 so my windows calc says 
Here.
HowlingUlf
let’s not talk signal to noise ratio here
How about just signal? Will a puny guitar output survive the journey with them all bypassed? I think there would have to be some relay stations… 
And all of it feeding into a lone Fender SuperReverb amp (4x10)
(with the ‘tilt-back’ legs).
Well at least the input seems to be going into the ‘dry’ channel.
{‘-’}
you can’t use that thing anyway, unless you are good at tap danicing in a mine field AND playing the guitar simultaneously. Some one did it for laughs! 
Where is my Sherlock award? 
You need this remote control unit…
Nice find, looks like it’s the same board
That’s outstanding (no pun intended)!
Who wants to tile their studio floor with Boss Pedals? 
Well, you do have to feed the kid I suppose, but at least he’s no longer in diapers! Just pack him into the road cases after the gig. 
Here’s Swamptone, carrying his pedals into the next gig…
If he were it would be Nappy You Hear.
2^96 = 79228162514264337593543950336 possible combinations…
That’s different. That figure is the highest number you can represent with 96 binary digits. 2x2x2x2x2… etc. The twos are all the same but the pedals are all different so each time you use one it’s not available in the next position.
Hence 96x95x94… etc.
Yeah, Mr duck is right. For every position on the board, you just check how many options you have. 96 for the first, 95 for the second etc.
This is how many combinations you can get by switching each pedal on/off AFTER you have chosen pedal positions from 96! possibilities.
So the total possible ways of connecting and using the pedal board is 96!*2^96 which is 7.86 *10^178.
Not bad 
What about pedals with stereo outs
If all pedals have mono inputs and you are not allowed to merge signals, then it’ll be less