If Jacob owns 12 books, how many different ways can he arrange 3 of these books on a single bookshelf

1320

Step-by-step explanation:

We will think as follows. Recall that at first, he chooses 3 books. Then, we want to see in how many ways he can arrange this books. For the first book, he has 3 options, for the second one 2 and for the third 1. Then, the total number of ways in which he can arrange 3 books is 3!. So we know that after choosing 3 books, he can arrange them in 3! ways. So, we want to check the total number of ways he can choose 3 books out of 12. That is given by the binomial coefficient . Then, the total number of ways of arranging 3 books is

Thus, he can arrange 3 books out of 12 in 1320 different ways

chase is right because he already been to the swings and he know how far it will be to get there

step-by-step explanation:

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