Permutation Problems

1. A secretary writes letters to A, B, C, and D. She also prepares four envelopes addressed to A, B, C, and D. She manages to put all the letters in the wrong envelopes. Enumerate (list) all the ways she can do that.
2. You have the following books that you would like to arrange on your shelf.
   • War and Peace by Leo Tolstoy
   • Anna Karenina by Leo Tolstoy
   • Magic Mountain by Thomas Mann
   • Death in Venice by Thomas Mann
   • Arms and the Man by Bernard Shaw
   • Candida by Bernard Shaw
   Enumerate the different ways you can arrange the books as long as you keep the books by the same author together.
3. A, B, C, D, and E go to a ball game. A and B want to sit next to each other but C and D prefer not to. Enumerate the different ways that they can sit on the same bench.

Combination Problems

1. Home owners A, B, C, D, E, and F have all agreed to serve on the Home Owners' Association. But the Home Owners' Association just needs three people. A is willing to serve only if B serves, though B has not made that same condition. C and D both refuse to serve if the other is in the association. Enumerate the different associations that you can form.
2. A side show at Coney Island is described as follows: There were ten little dummies which you were to knock over with baseballs. The man said: "Take as many throws as you like at a cent apiece and stand as close as you please. Add up the numbers on all the men that you knock down and when the sum amounts to exactly fifty, neither more nor less you get a genuine 25 cent Maggie Cline cigar with a gold band around it." The numbers on the ten dummies were: 15, 9, 30, 21, 19, 3, 12, 6, 25, 27 What numbers in that series add up to 50?