How many positive, five-digit integers contain the three-digit block “123”? Two such integers are 12,350 and 41,232.
+128408 123 in the first through third positions, we have (00 - 99) in the last two positions = 100 integers
123 in the second position through fourth positions, we have (1 - 9) in the first position and ( 0-9) in the last position
So 9 * 10 = 90 integers
123 in the last three positions we have (1 - 9) in the first position and (0 - 9) in the second position
So 9 * 10 = 90 integers
So
100 + 90 + 90 =
280 integers
