A12-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

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

what are the statments

step-by-step explanation: