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

(UPSC CSAT – 2022)

1. 72
2. 81
3. 90
4. 100

Solution: Ans.(a)

X,Y ϵ {1, 2, 3, 4, 5, 6, 7, 8, 9}

To fill place of X there is 9 ways

To fill place of Y there is 8 ways

Number of numbers = 9×8 = 72