What is the number of numbers of the form 0.xy, where x and y are distinct non-zero digits?

Explanation:

1. Identify the set of non-zero digits: The non-zero digits are {1, 2, 3, 4, 5, 6, 7, 8, 9}. There are 9 such digits.

2. Determine choices for x: Since x must be a non-zero digit, there are 9 possible choices for x.

3. Determine choices for y: Since y must also be a non-zero digit AND distinct from x, one of the 9 non-zero digits has already been chosen for x. Therefore, there are 9 - 1 = 8 remaining non-zero digits for y.

4. Calculate the total number of numbers: To find the total number of possible combinations for 0.xy, multiply the number of choices for x by the number of choices for y. Total numbers = (Choices for x) * (Choices for y) = 9 * 8 = 72.

Therefore, there are 72 such numbers.

Analyzing the options: A) 72: This matches our calculation, considering x and y are distinct non-zero digits. B) 81: This would be 99, if x and y could be the same non-zero digit. C) 90: This would be 109, if x could be any digit (0-9) and y any distinct digit (0-9), but x and y must be non-zero. D) 100: This would be 10*10, if x and y could be any digit (0-9) and could be the same.

The final answer is A.