A 12-volume numbered set of books is placed randomly on a shelf. What is the probability that the books will be numbered in the correct order from left to right?

Step-by-step explanation:

There is a 1/12 probability that volume 1 will be correctly put in position 1.

If we assume that volume 1 is right, then since there are then only 11 books left to choose from, there is then a 1/11 prob that volume 2 will be in position 2. And so on. By the same reasoning there is 1/10 prob that volume 3 is then right, 1/9 prob for volume 4, 1/8 prob for volume 5, and 1/7 prob for volume 6,

and 1/6 prob for volume 7, and 1/5 prob for volume 8, and 1/4 prob for volume 9, and 1/3 prob for volume 10, and 1/2 prob for volume 11, and 1/1 prob for volume 12.

So the probability is 1 / (12*11*10*9*8*7*6*5*4*3*2*1) = 1 / 479,001,600 ...