6 periods and 5 subjects
2
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? Is the answer 1800 or 3600 ? I am confused. Initially this appeared as a simple question. By goggling a bit, I am stuck with two answers. Different sites gives different answers and am unable to decide which is right. Approach 1 (Source) we have 5 sub and 6 periods so their arrangement is 6P5 and now we have 1 period which we can fill with any of the 5 subjects so 5C1 6P5*5C1=3600 Approach 2 (Source) 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!