Main post link -> http://blog.brilliant.org/2013/01/09/permutations-ii/
Samir and Mirdula each have distinct 7 books that they want to display on their shelves. Mirdula has lots of room on her shelf, however, Samir only has room to put 6 of his 7 books. Assuming that they fill up the entire shelf, who has more possible ways to arrange the books on their shelf? Why is this the case?
A waiter at a restaurant takes the drink order for a table of ten people but forgets to write down who ordered which drink. The orders are 5 cups of coffee, 3 glasses of water, 1 glass of milk, and 1 apple juice. How many different ways can the waiter deliver the drinks to the customers so that each customer gets one drink?
Consider all the ways to rearrange the letters of the word CALVIN, and arrange them in alphabetical order. In what position will CALVIN appear in? How about NIVLAC?
(*) Lisa wants to arrange 7 ornaments on her mantle. She has 2 identical cats, one mouse and 4 other different ornaments. If the mouse cannot be next to either of the cats, how many ways can they be arranged? Hint: Principle of Inclusion and Exclusion.