The composer Beethoven wrote 9 symphonies, (a) How many ways are there to play first a Beethoven symphony and then a Beethoven piano concerto? ways (b) The manager of a radio station decides that on each successive evening (7 days per week), a Beethoven symphony will be played followed by a Beethoven piano concerto followed by a Beethoven piano sonata. For how many years could this policy be continued before exactly the same program would have to be repeated? (Assume there are 365 days in a year. Round your answer up to the nearest who number.) years

At a carnival, an individual can win a prize by choosing a rubber duck from a pond with "Win" written on the underside of the duck. There are a total of eight ducks with "Win" written on the underside of the duck, and there are 17 ducks with "Lose" written on the underside of the duck. After each pick, if a prize is won, the duck is replaced in the pond. If a prize is not won, then the duck is again placed back into the pond. If an individual makes four picks, what is the probability the individual will win a prize exactly one time? (4) (0.32) (0.68) 1! 4! (0.32)¹ (0.68)³ O2(0.32)(0.68) (0.32) (0.68)³

A bagel shop has a selection of 8 different kinds of bagels (at least 10 of each). (.1) How many different selections of 10 bagels can be made? ( .2) If garlic is one kind of available bagel and onion is another, how many different selections of 10 bagels can you make so that you have at least 3 onion bagels and exactly 2 garlic bagels?

There are nine different positions on a baseball team. If a team has 15 players how many different line-ups can the team make? (Assume every player can play every position.) The team can make different line-ups. Baseball games consist of nine innings. A team wants to change its line-up every inning. If no game goes to extra innings, and a season consists of 135 games, how many complete seasons can the team play without repeating a line-up? The team can play complete seasons without repeating a line-up. (Your answer should be an integer.)

A mutual fund has 16 stocks in its portfolio. On a given day 6 stocks move up, 4 stay the same and 6 move down. In how many ways could this happen?

Suppose you have 11 books and you randomly pick 3 to take on vacation with you. How many ways can you do this?

A father and his three children decide to hold a vote to select an after dinner activity. They will either see a play or a movie. If the majority of the family agrees on a preferred activity, then they will do that activity. If two family members vote to see a play and the other two family members vote to watch a movie, then (since the father will pay for the activity), the father's vote will be used to break the tie. (a) How many winning coalitions are there in this situation? (b) Find one of the children's Banzhaf power index.