There are six periods in each working day of a school. Find the number of ways in which 5 subjects can be arranged if each subject is allowed at least one period and no period remains vacant.

Explanation

Let the five subjects are a, b, c, d, e. Since the number of subjects are less than the number of periods, any one of the five subjects will occur twice.
If subjects a occurs twice (a, a, b, d,d,e), then six subjects can be arranged in `(6!)/(2!)=360`
Now subject b, c, d or e may also repeat.
So, total number of ways `=5xx360=1800`.