There are 6periods in each working day of a school. In how many ways can 1 arrange 5subjects such that each subject is allowed at least 1period?
Choose the correct choice from the following answers:
A) 1200
B) 1800
C) 2000
D) 2500
E) 2600
5 subjects can be arranged in 6 periods in 6P5 ways.   Remaining 1 period can be arranged in 5P1 ways.   Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.   Total number of arrangements = (6P5 x 5P1)/2! = 1800   Alternatively this can be derived using the following approach.   5 subjects can be selected in 5C5 ways.   Remaining 1 subject can be selected in 5C1 ways.   These 6 subjects can be arranged themselves in 6! ways.   Since two subjects are same, we need to divide by 2!   Total number of arrangements = (5C5 × 5C1 × 6!)/2! = 1800   1800
<result>B</result>
There are 6periods in each working day of a school. In how many ways can 1 arrange 5subjects such that each subject is allowed at least 1period?