> Based on current engine failure rate, that's (17/18)^9 + (1/18)^8 + C(9,2)...

> Based on current engine failure rate, that's (17/18)^9 + (1/18)^8 + C(9,2) * (1/18)^2 * (17/18)^7

I think the second part of that calculation is incorrect. I'm getting:

  P(0 engine fail) = (17/18)^9 ~= 0.5978
  P(1 engine fail) = (17/18)^8 * (1/18) * C(9,1) ~= 0.3165
  P(2 engine fail) = (17/18)^7 * (1/18)^2 * C(9,2) ~= 0.0745

Adding those together gives:

  P(<=2 engine fail) = (17/18)^9  +  (17/18)^8 / 2  +  (17/18)^7 / 9 ~= 0.9888

That's the same answer you came up with, so I guess you have the correct calculation written down somewhere. Moving to 3 or more engine fails then gives:

  P(>=3 engine fail) = 1 - P(<=2 engine fail) ~= 0.0112