Independent sets Statistic problem

Question

Probability played a role in the rigging of the April 24, 1980, Pennsylvania state lottery (The Los Angeles Times, September 8, 1980). To determine each digit of the three digit winning number, each of the numbers 0,1,2,. . . ,9 is placed on a ping pong ball, the ten balls are blown into a compartment and the number selected for the digit is the one on the ball that floats to the top of the machine. To alter the odds, the conspirators injected a liquid into all balls used in the game except those numbered 4 and 6, making it almost certain that the lighter balls would be selected and determine the digits in the winning number. Then they proceeded to buy lottery tickets bearing the potential winning numbers. How many potential winning numbers were there (666 was the eventual winner)?

Answer 1

I think I got it. If anyone can check this for me that would be awesome!

It is ordered with replacement.

Let x be the number chosen

p(x=6) = 1/2 = .5
p(x=6) for three times = (.5)^3 = .125

Answer 2

Correct. There are 8 permutations that feature the numbers $4$ and $6$.

{4,4,4} {4,4,6} {4,6,4} {4,6,6} {6,4,4} {6,4,6} {6,6,4} {6,6,6}