According to Bulbapedia, there are 559 moves in the game. Smeargle can sketch all but struggle and chatter. He also probably wouldn't carry sketch for a battle, so I won't count that. That leaves 556 moves total for him to learn. nCr=n!/(r!(n-r)!). n=556 and r=4, making 3,939,049,415 possible combinations for a smeargle moveset.