I'm the opposite: moarr tools
Sometimes I use permutations when using a calculator without an nCr function because it's fewer keystrokes when I don't have to divide by a factorial. C(n,r) = nPr / r!
Or occasionally they're more efficient regardless, for instance the chance of an unpaired flop is 48*44/51/50, which is nicer than doing C(13,3)*4³ / C(52,3)
GSX has to be multiplied by 3!
For GSS, by using perms you already counted the 2! ways to arrange the S's, so now you just need to multiply by the 3 ways to place the G among the S's. Same thing for GGS.
Then for the denominator use 27*26*25
After those adjustments, there is a factor of 3! present in both the numerator and denominator.
Having to make those multiplications is the drawback of permutations, which is why combos are usually simpler (when order doesn't matter), esp when you have the nCr function available (or the "choose" function in a google search or wolfram|alpha).
Some people like to multiply fractions together (compound probabilities) without worrying about combos or perms. Those same multiplications are necessary when doing that, because fractions are algebraically the same as dividing perms by perms. For instance:
P(GSS) = 3(2*9*8) / (27*26*25)
or P(GSS) = 3(2/27)(9/26)(8/25)