In how many ways can 7 science books, 3 history books, and 6 mathematics books be arranged on a shelf if books of the same subject must remain together (all books are distinct)? (Hint: First arrange the books for each subject, then arrange the order of the subjects.)

Bob owns 7 different books. He wants to arrange all of these books left-to-right on a single bookshelf. How many distinguishable ways can Bob do this?

Jessica is grocery shopping and has 16 cherry tomatoes and 12 grape tomatoes in her shopping basket. When she gets home, she prepares her ingredients for lunch, but she forgets which of the tomatoes are cherry and which are grape. She cannot distinguish between the two types of tomatoes, so she just picks 13 tomatoes. How many different sets of 13 tomatoes are possible if there are exactly 7 cherry tomatoes?

In the local boating pond there are 10 plain wooden boats, each with a different number. The owner decides that some of these boats will be painted: one in blue, one in green, one in red, and one in orange, and the remaining ones left unpainted. How many ways are there to paint the boats? The number of ways is