First the total no of cases is 6!/3!3! (Since there is only 2 outcomes ,hit or miss,and they are in equal proportion ,3 times,by the question). Now the no of favourable outcomes is5!/ 2!3!(since the last fire is confirmed hit.

The answer getting is 1/2 for thee above method. When you multiply it by the probability of hitting you get 0.165 .

I'm not sure about the step may be this get you the closest range.

By your clue of range the only answer possible is 0.0659 since it is the only term b/w the given range.