If I interpret your code correctly, you are doing things the hard way. Your expression for Pfa is simply the binomial expansion of ((Pfa1+(1-Pfa1))^M without the first term where i is equal to zero. Hence, you are trying to solve
(Pfa1 + (1-Pfa1))^8 = 1 = 10^(-6) + (1-Pfa1)^8
whose solution is easily found as
Pfa1 = 1 - 0.999999^(1/8)
Probably the cause of your error message is the reference to the numeric function ‘nchoosek’.