Explanation

(c)
The first digit $a$ can take any one of 1 to 8
The third digit $c$ can take any one of 0 to 9
When $a =$1, $b$ can take any one of 2 to 9=8 values
When $a = 2$, $b$ can take any one of 3 to 9=7 values
When $a = 3$, $b$ can take any one of 4 to 9=6 values
$\cdots\ \ \ \cdots\ \ \ \cdots\ \ \ \cdots$
$\ \ \ \ \cdots\ \ \ \cdots\ \ \ \cdots\ \ \ \cdots$
When $a = 8,\ b$ can take any one $(b = 9) = 1$ values Thus, the number of total numbers
$= (8 + 7 + 6 + ... + 2 + 1) \times 10 = \frac{8 \times 9}{2} \times 10 = 360$