Question

How many ways can six different books be arranged on a shelf if one of the books is a dictionary and it must be on an end?

Short answer

There are240 waysthe books can be arranged on a shelf.

Step-by-step solution

Step 1. Given Information.

It is to be determined how many ways can six different books be arranged on a shelf if one of the books is a dictionary and it must be on an end.

Step 2. Calculation.

Since the dictionary is always on an end, considering that it is on one end the remaining 5 books are to be arranged.

When one of the 5 books is placed, 4 remain to be arranged in the next place, then 3 and so on.

By the Fundamental Counting Principle, there are $5\times 4\times 3\times 2\times 1=120$ different ways the 6 books can be arranged if the dictionary is considered on one particular end.

Similarly, the dictionary can also be placed at the other end and hence there are 120 more ways.

Step 3. Conclusion.

Hence, by Fundamental Counting Principle, there are 240 ways the books can be arranged on a shelf.