Question

An author has six different book in print. If those six books are stacked in random...

An author has six different book in print. If those six books are stacked in random order, what is the probability that they are arranged in alphabetical order from top to bottom? How about seven different books?

Homework Answers

Answer #1
  • We have 6 options for the first book we place on the shelf
  • Once we've already placed the first book, we have 5 remaining options for the second book
  • Then, 4 options for the third
  • Then, 3 options for the fourth
  • Then, 2 options for the fifth
  • Then, only 1 option for the sixth

Multiplying the options for each slot together gives us the total possible arrangements. This would be .

Answer: there is only one desired outcome, or one way to arrange these books in alphabetical order. However, there are 6! = 720 ways to arrange them, so the probability that they will be in alphabetical order is:

P = 0.00139

For 7 books:

P = 1/7! = 0.000198

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