What is the probability that no 1s will be in the output for an input sequence of 10 digits?

The total numbers with 10 digits are 9*10*10*10*10*10*10*10*10*10 = 9 * (10^9)

If you are restricted to use no 1s, the numbers are 8 * (9^9)

Then, the probability is : numbers with no 1s / total numbers

= 8 * (9^9) / [9 * (10^9) ] = 0.344