There are six periods in each working day of a school. The number of ways in which 5 subjects can be arranged such that each subject is allotted at least one period and no period remains vacant is

Step-by-step solution

Select one subject which is to be repeated in C 1 5 ways Select two periods in which the selected subject will be taught in C 2 6 ways Remaining 4 subjects will be taught in 4 periods in 4 ! ways. ⇒ Required number of ways = C 5 1 × C 6 2 × 4 ! = 5 × 15 × 24 = 1800