Among the integers from 1 to 10, 000, 000, 000 which are there more of: Those in

Question

which the digit 1 occurs or those in which it does not occur?

Answer 1

number without a 1
= 9^7
= 4,782,969

so number where no 1 occurs = 4,782,969
number where a 1 does occur = 10,000,000-4,782,969
= 5,217,031

Answer 2

how do you prove this?