Chapter 8, Problem 76CR

To determine

To find: the probability that the books are shelved in the correct order.

Answer to Problem 76CR

The probability that the books are shelved in the correct order = $\frac{1}{120}$ .

Explanation of Solution

Given information: A child returns a five-volume set of books to a bookshelf. The child

is not able to read and so cannot distinguish one volume from another.

Formula used:

Formula for the number of combinations of n numbers taken r numbers at a time is,

  $n(S){=}_n{C}_r.$

If an event has n(E) equally likely outcomes and its sample space S has n(S) equally likely outcomes, then the probability of event is given by,

  $P(E)=\frac{n(E)}{n(S)}.$

Calculation:

There are five-volume set of books and to choosing 1 from 5, the number of possible combination is,

  $n(S){=}_n{C}_r{=}_5{C}_1=\frac{5\times 4\times 3\times 2\times 1}{1}=120.$

Only a single outcomes will give the correct order, so the equally likely outcomes are,

n (E) =1.

So,

  $P(E)=\frac{n(E)}{n(S)}=\frac{1}{120}.$