Math integers hardest OMG

Question

An integer from 100 through 999 inclusive is to be chosen at random what is the probability that the number chosen will have 0 as least 1 digit

Answer 1

100-110

120,130,140,150,160,170,180,190

200-210

220,230,240,250,260,270,280,290

300-310

320,330,340,350,360,370,380,390

400-410,

420,430,440,450,460,470,480,490

see a pattern? I hope so because it holds for

the 500, 600, 700, 800, 900

So that's 19 per group.

19 x 9 = 171

171/ (999-100+1) =

171/ 900 =

0.19