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Chapter 23 Balls in Boxes Part 1
Answer the following questions by turning each problem into a balls in boxes problem. (What are the balls? What are the boxes?)
Exercises Practice Problems
1. Puppies!
How many ways are there to give four doggie treats to six puppies, with no more than one doggie treat to each puppy?
How many ways are there to give four doggie treats to six puppies when you can give multiple treats to the same puppy?
2. Stars.
How many ways are there to put a star sticker (they come in gold, silver, red, green, and blue) on every student's paper in a class of 30 students?
3. Fruit Selection.
How many ways are there to buy 10 pieces of fruit, when you can choose between four kinds: apples, bananas, oranges and pears? (Note: if we buy 2 apples, we treat the apples as "the same.")
4. An Extra Slice of Pie.
How many ways are there to give 4 slices of apple pie and 6 slices of pumpkin pie to nine hungry diners, where each diner gets exactly one slice of pie. (So there is one slice left over!)
5. Spooky Minifigs.
How many ways are there to arrange 6 identical ghost figurines and 9 identical zombie figurines on a shelf?
How many ways are there to arrange 6 distinct ghost figurines and 9 distinct zombie figurines on a shelf?
6. Toys for Tots.
How many ways are there to give three distinct toys to three out of five children, such that no child gets more than one toy?