8. (15 points) Let n be a randomly chosen 7-digit positive integer.

(a) What is the probability that n is even?

(b) What is the probability that n ? 7, 000, 000?

(c) What is the probability that 1, 500, 000 ? n ? 6, 200, 000?

(d) What is the probability that n does not contain repeated digits and is not made of digits 0 and 5?

(e) What is the probability that n has no repeated digits and is divisible by 5?

9. (15 points) In a box of 25 light bulbs, 15 of them are defective and the rest are working.

(a) In how many different ways can we pick 7 light bulbs from the box?

(b) If we randomly pick eight light bulbs, what is the probability of picking no defective light bulbs?

(c) If we randomly pick nine light bulbs, what is the probability of picking five or seven defective light bulbs?