A whole number is called decreasing if each digit of the number is less than the digit to its left. For example, 8540 is a decreasing four-digit number. How many decreasing numbers are there between 100 and 500 ?
(A) 11
(B) 10
(C) 9
(D) 8
(E) 7
The easiest way to count these numbers is to list them by considering their hundreds digit.

Hundreds digit of 1: No such numbers, since tens digit must be 0 , which leaves no option for units digit.

Hundreds digit of 2: Only one possible number, namely 210.

Hundreds digit of 3: Here the tens digit can be 2 or 1, giving numbers 321, 320, 310 .

Hundreds digit of 4: Here the tens digit can be 3,2 or 1, giving numbers 432, 431, 430, 421, 420,410 .

Therefore, there are 10 such numbers in total.

ANSWER: (B)