Question 256025
FIrst we have to find the total number of integers in the set: 999-100+1 = 900.
Next we need an organized way to determine our successful options: 0 in at least 1 digit.
0 in 3 digits: 
0
0 in 2 digits: 
100, 200, 300, 400, 500, 600, 700, 800, 900 = 9
0 in 1 digit: 
101 - 110, 120, 130, 140, . . ., 190: 18
201 - 210, 220, 230, 240, . . ., 290: 18
. . .
901-910, 920, 930, 940, . . . 990: 18
or 18*9 = 162
Now 0 +9 + 162 = 171
So the probability is
171/900 = 19/100