There is a new boss in the office There are 7 men and 5 wome

There is a new boss in the office There are 7 men and 5 women that work in the office. His raises vary: $10,000 for the first name, $3,000 for the second name, $2,000 for the third.

(a) Suppose he gives the first raise to a man, and the next two to women. How many ways can he decide on raises? (at most one raise per person)

(b) If Alice and Bob both get raises then how many ways can he decide on raises? (the man / woman / woman condition no longer applies) New Rules! Your new boss decides that he doesn’t care if he gives all three raises to the same person. He picks a name from a hat, records them for a raise, then returns the name to the hat before picking again (so he might choose someone more than once).

(c) Suppose he gives the first raise to a man, and the next two to women. How many ways can he decide on raises?

(d) What is the probability that he gives all three raises to the same person?

(e) What is the probability that he gives one raise to a man (and two to women)?

(f) Suppose that Alice and Bob’s names are on slightly larger pieces of paper, so that each time there is a 10% chance your boss picks Alice, a 10% chance he picks Bob, and an 8% chance for each of the other 10 employees. What is the chance that Bob gets exactly one raise and Alice gets none?

Solution