How many ways can a librarian arrange 15 books on a shelf if she has 20 books?

More than you'd believe! The first book can be any one of twenty, the second any one of the remaining nineteen and so on until the fifteenth book can be any of the last six.

This is 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 different arrangements, which multiplies to a 17-digit number!

20,274,183,401,472,000 or "twenty quadrillion, two hundred and seventy four trillion, one hundred and eighty three billion, four hundred and one million, four hundred and seventy two thousand" (in US figures).

Do not attempt to check it in your local library!