A Fun Way to Spend the Next Two and a Half Million Years

“If you own fifteen books, and if you would like to arrange them on a shelf in all the possible arrangements, and if you would need only one minute for each arrangement, the whole job will take you nearly two and a half million years.”

— Isaac Asimov’s Book of Facts

Would you like to see how to come up with two and a half million years?

Well, when placing the first book on the shelf, you have 15 choices to select from. Once the first book is placed, now you will have 14 books to choose from in the second position, then 13 books, and so on, until you are left with one one choice in the last position. Using the Fundamental Counting Principle, multiply:

15 ∙ 14 ∙ 13 ∙ 12 ∙ 11 ∙ 10 ∙ 9 ∙ 8 ∙ 7 ∙ 6 ∙ 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1
= 15!
= 1,307,674,368,000 ways

If you take 1 minute for each arrangement, then you will need 1,307,674,368,000 minutes to complete the entire task. Now let’s convert minutes first into hours, then into days, then into years:

1,307,674,368,000 minutes ÷ 60 minutes = 21,794,572,800 hours
21,794,572,800 hours ÷ 24 hours = 908,107,200 days
908,107,200 days ÷ 365 days ≈ 2,487,965 years
Which is nearly 2 and a half million years.