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?  Choices: A) 1800 B) 3200 C) 2600 D) 3600 E) None of these
There are 5 subjects and 6 periods. Each subject must be allowed in at least one period. Therefore, two periods will have same subject and remaining four periods will have different subjects.   Select the two periods where the same subject is taught. This can be done in 6C2 ways.   Allocate a subject two these two periods(5C1 ways).   Remaining 4 subjects can be arranged in the remaining 4 periods in 4! ways.   Required number of ways   = 6C2 × 5C1 × 4! = 1800   1800nswer : 1800.
<result>A</result>
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?