Nine people are going on a skiing trip in 3 cars that hold 2, 4, and 5 passengers respectively. In how many ways is it possible to transport the 9 people to the ski lodge using all cars?

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?

At Rosemont High School, 14 players are on the varsity basketball team, 35 players are on the varsity football team, and 7 of these players are on both teams. How many different individual players are on the two varsity teams?

Alice and Bill have four grandchild, and they have three framed pictures of each grandchild. They wish to choose one picture of each grandchild to display on the piano in their living room, arranged from oldest to youngest. In how many ways can they do this?

Alice and Bill have four grandchildren, and they have three framed pictures of each grandchild. They wish to choose one picture of each grandchild to display on the piano in their living room, arranged from oldest to youngest. In how many ways can they do this?

A palette of water color paints has 3 shades of green, 3 shades of blue, 2 shades of red, 2 shades of yellow, and 1 shade of black. How many ways are there to choose one shade of each color?

A rock group needs to choose 3 songs to play at the annual Battle of the Bands. How many ways can they choose their set if have 15 songs to pick from?

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

At a carnival, $2,914.25 in receipts were taken at the end of the day. The cost of a child's ticket was $20.50, an adult ticket was $29.75, and a senior citizen ticket was $15.25. There were twice as many senior citizens as adults in attendance, and 20 more children than senior citizens. How many children, adult, and senior citizen tickets were sold?

A commuter must travel from Ajax to Barrie and back every day. Four roads join the two cities. The commuter likes to vary the trip as much as posible, so she alwaysleaves and returns by different roads. In how many different ways can she make the round-trip?