1) Player A, B, and C play a quiz game. For each question, a player who rings a buzzer first has an opportunity to answer the question. For each question, only one player can answer the question, and player A, B, and C have 20%, 30%, and 50% chance of ringing the buzzer respectively. Once given an opportunity to answer, player A, B, and C have 50%, 40%, and 30% chance of making the right guess respectively. Questions are independent to each other, and every question is answered. (a) Once a question is asked, find the probability that player A gives the correct answer. (b) Once a question is asked, find the probability that the answer is correct. (c) Find the probability that given that the answer is correct, the player who answered it is A.

Over the past year, John has purchased 30 books. In how many ways can he pick four of these books and arrange them, in order, on his nightstand bookshelf? In how many ways can he choose four of these books to take with him on his vacation at the shore?