On each working day of a school there are six periods. The number of ways in which five subjects are arranged if each subject is allotted at least one period and no period remains vacant is

Step-by-step solution

There are 6 periods and 5 subjects. Each subject must be allotted at least one period. Since there are 6 periods and 5 subjects, exactly one subject must be allotted two periods, and the remaining four subjects must be allotted one period each. First, choose the subject that will be allotted two periods. This can be done in ⁵C₁ = 5 ways. Next, choose the two periods out of 6 that will be assigned to this subject. This can be done in ⁶C₂ = 15 ways. The remaining 4 periods are to be assigned to the remaining 4 subjec