One day, Jeff decides that he is a master of all things sushi and decides to open a sushi restaurant.

Despite his faith in his skills, it turns out that Jeff only knows how to make three different types

of sushi, Kangaroo sushi, Lamb sushi and Beer sushi. Jeff constructs a business plan based upon

some assumptions. He assumes that each customer will order exactly 10 pieces of sushi, each of

the ten pieces are chosen one at a time, and each choice is independent of all other choices. He

assumes that 20% of all choices will be for Kangaroo, 30% for Lamb, and 50% for Beer.

(a) Based upon Jeff's assumptions, what is the probability that a customer will order 3 pieces

of Kangaroo sushi?

(b) What is the expected number of Kangaroo or Lamb sushi pieces that a customer will order?

(c) Unsurprisingly, when Jeff's first customer arrives, Jeff has not finished preparing enough

food, and he only has 5 Kangaroo sushi, 8 Lamb sushi and 7 beer sushi ready. It also

turns out that all of Jeff's sushi looks equally unappetising, so the customer just chooses

10 different pieces completely at random, that is, each of the 20 available pieces are equally

likely to be chosen. What is the probability that Jeff will have no more Kangaroo sushi

after the first customer's order?