What is the number of numbers of the form 0·XY, where X and Y are distinct non-zero digits?

The numbers are of the form 0.XY, where X is the digit in the tenths place and Y is the digit in the hundredths place. 1. Identify the possible digits for X and Y: Both X and Y must be non-zero digits. This means they can be any digit from {1, 2, 3, 4, 5, 6, 7, 8, 9}. There are 9 such digits. 2. Determine the number of choices for X: Since X must be a non-zero digit, there are 9 possible choices for X (any digit from 1 to 9). 3. Determine the number of choices for Y: Y must also be a non-zero digit, AND it must be distinct from X. Since one non-zero digit has already been chosen for X, there are 8 remaining non-zero digits that Y can be. 4. Calculate the total number of combinations: To find the total number of such numbers, multiply the number of choices for X by the number of choices for Y. Total = (Choices for X) * (Choices for Y) = 9 * 8 = 72. Therefore, there are 72 such numbers. The final answer is A) 72.