16) Coach Otis Campbell offered to buy hot dogs for players on his team. Of the 44 players: 6 wanted all three condiments 11 wanted ketchup and relish 10 wanted ketchup and mustard 8 wanted mustard and relish 28 wanted ketchup 20 wanted mustard 14 wanted relish (a) How many wanted ketchup only?

A large research project is looking for more researchers. There are 8 spots open on the research team. There are 10 mathematicians and 14 computer scientists that apply for the team. a. How many different ways can a team of 8 be made for the project? b. How many different ways can a team of 8 be made for the project if the team must contain at least one computer scientist and at least one mathematician.

Three hungry pirates, Ahab, Bluebeard, and Hook, were stranded on a desert island. They came upon a treasure chest, which they immediately opened. To their joy, they found it to be full of pretzels! Immediately they each ate 10, then they decided they should save the rest for later. That night, after the others had fallen asleep, Ahab crept to the treasure chest and opened it. He separated the pretzels into 3 equal piles. There was 1 extra pretzel, which he gave to a passing monkey. Then he stole one of the 3 equal piles of pretzels, put the rest back into the chest, and went back to camp. A short time later Bluebeard sneaked over to the chest. He separated the pretzels into four equal piles (he wasn’t quite as greedy as Ahab). There were 2 extra pretzels, which he gave to a passing monkey. He then stole one of the four piles and put the rest back into the chest. Still later Hook went to the chest and separated the pretzels into five equal piles. There were 3 left over, which he gave…

1. You just won 4 tickets to a concert, but you have 8 friends who would like to go with you. How many different ways can you give out the extra 3 tickets to your friends? 2. The booster club has 10 people running for the offices of president, vice-president, secretary and treasurer. How many ways can the offices be filled?