# Bomb The Target! Part 3

A Lockheed Martin F-22 Raptor has gone on a mission to bomb an old military hideout . Three bombs are dropped in succession at it .

The probabilities of a hit in the first shot is $$\frac{1}{2}$$ , in the second is $$\frac{2}{3}$$ and in the third is $$\frac{3}{4}$$ .

In case of one hit , the probability of destroying the target is $$\frac{2}{3}$$ , in case of two hits is $$\frac{7}{11}$$ and in case of three hits is $$1$$ .

Find the probability of destroying the hideout in three shots .

The answer is of the form $$\frac{f}{g}$$ where $$f$$ and $$g$$ are co-prime numbers ;

Report the last three digits of $$f^{g}$$ .

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