[Math Lair] Permutations Worksheet

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You may want to read Permutations and Combinations before doing this worksheet.

  1. How many ways are there of arranging eight books on a shelf?
  2. If each arrangement of books takes one minute (on average) to set up, how long will it take to try all possible arrangements?
  3. How many different ways are there of selecting two cards at random from a 52-card deck?
  4. How many ways are there of arranging the Ace, Two, and Three of Hearts and the Four, Five, Six, and Seven of Diamonds such that all cards of the same suit are together?
  5. How many permutations (arrangements) of the digits 1 through 9 are there such that even and odd digits alternate? (Hint: Try breaking the problem up.)