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

What is the number of numbers of the form 0.XY, where X and Y are distinct non-zero digits?
  1. 72
  2. 81
  3. 90
  4. 100

Solution

X and Y are distinct non-zero digits, so X has 9 choices (1-9) and Y has 8 remaining choices. Number of numbers of the form 0.XY = $9 \times 8 = 72$.

Asked in: CSAT 2022

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