CAYLEY 2022 Problem 14

The integer 48\:178 includes the block of digits 178. The three integers 51\:870,19\:728 and 38\:717 do not include the block of digits 178 . How many integers between 10\:000 and 100\:000 include the block of digits 178?

Answer Choices
A. 280
B. 300
C. 270
D. 310
E. 260