Question

There are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period ?

• A. $3200$
• B. $1800$
• C. $3600$
• D. none of these

Answer 1

The correct option is B $1800$

5 subjects can be arranged in 6 periods in $6_{P_5}$ ways.

Any of the 5 subjects can be organized in the remaining period ($5_{C_1}$ ways).

Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.

Total number of arrangements = $\frac{6_{P_5}\times 5_{C_1}}{2!}=1800$