Problem
COM-B1-M02-P017 Three Books in a Prescribed Order
#17
★★★☆☆ Level 3 of 5
There are \(8\) distinct books on a shelf. In how many ways can they be arranged so that books \(A,B,C\) appear in the order \(A\) before \(B\) before \(C\), not necessarily consecutively?
Among the \(3!\) relative orders of \(A,B,C\), exactly one works.
There are \(8!\) arrangements. The relative orders of \(A,B,C\) are equally likely, and there are \(3!=6\). Exactly one order works, so the answer is \(8!/6=6720\).
Again emphasizes “before” versus “adjacent”.