How many numbers are there between 500 and \(600\) in which \(9\) occurs only once?
Well, why don't you just list the numbers with one "9" in them?
509, 519, 529, 539, 549, 559, 569, 579, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598 ==18 such numbers.