Find the probability that no two dice show the same face

[BrownianMan]

3. Three indistinguishable (fair) dice are thrown simultaneously at random.
(a) Find the probability that no two dice show the same face (the same number).
(b) Find the probability that the sum of the three dice is less than six and that no two dice show the same face (the same number.

Ok, so I got these, however, not sure what to do for this part:

(c) Describe the probability space, that is, the sample space, the event space, and the probability measure P you used in 3(a) and 3(b) above.

Would the sample space be the same as the outcome space, ie {1,2,3,4,5,6}^3?

The Long Shot Golf Ball Company determined that, on average, one percent of the balls they produce are defective.
(a) Find the probability that, out of 100 balls, at least one ball is defective.
(b) Find the probability that, out of 100 balls, at most one ball is defective.

For (a) I get 0.63.

For (b) I think I need to add P(zero defects) + P(one defect). I have P(zero defects) = 1-0.63=0.37, but not sure how to get P(one defect). If I use the binomial formula, I get a number larger than 1.

 

[lippyka]

Sample space = {0,1,2,...,100} Event space = {x|x>=1}, {x|x<=1} Probability measure P: P(x) = (1-0.01)^(n-x)*(0.01)^x for x=0,1,2,...,100