Question

If there are 6 periods in each working day of a school, then the number of ways that you can arrange 5 subjects during the working day is

• A. 600
• B. 720
• C. 1800
• D. 1325

Answer 1

The correct option is C 1800

5 subjects can be arranged in 6 periods in ${6_P}_5$ ways.

Remaining 1 period can be arranged in ${5_P}_1$ ways.

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

Total number of arrangements = $\frac{({6_P}_5\times {5_P}_1)}{2!}=1800$