I hope you enjoyed your summer math problems. Here are the solutions to the final set.
Jennifer just went back to school shopping. She bought 7 shirts, 5 pairs of pants, 4 pairs of fancy socks, sneakers and sandals. How many different outfits can Jennifer put together if she always wears one shirt, one pair of pants, one pair of shoes and she always wears socks with sneakers but never wears socks with sandals?
George is taking five classes this year: Math, Science, History, English, and Spanish. He needs a spiral notebook and a pocket folder for each class. Spiral notebooks come in 10 colors (black, blue, red, green, lime, purple, pink, orange, aqua, and yellow). Pocket folders come in six colors (blue, red, green, yellow, purple, and orange).
a) How many different ways can George choose the notebooks and folders for his classes if he doesn’t buy any duplicate items?
b) How many ways can George choose the notebooks and folders if he wants to have the same color notebook and folder for a certain class?
George is going to arrange his books, folders, and notebooks on the bookshelf. For each of five subjects he has a textbook, a folder, and a spiral notebook. He wants to be able to find things so he is considering different ways of organizing them.
a) How many ways can he arrange them if he keeps all three items from one subject together (the three math items are together in any order, the three history items, etc.)?
b) How many ways can he arrange them if he keeps all the textbooks together, all the spiral notebooks together, and all the folders together?