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There are six periods in a day and five subjects how many arrangements can be made such that each subject is taken atleast once

all 24 hours or how many hours are give?


The ans ( i suppose ) is 600...

we have 5 subjects to be arranged in 6 periods such that each subject is taken at least once.So naturally one subject is to be repeated. so one the periods can be occupied in 5 different ways.now that one subject is to be repeated , another period can also be filled in 5 different ways. Now having filled two of the periods with the same subject , we have 4 subjects left . So the next period can be filled in 4 different ways.proceeding this this way, the next period can be filled in 3 ways ,the next in two ways and the last in 1 way.(this completes all 6 periods)

so the total number of possible arrangements = 5*5*4*3*2*1 = 600

THEREFORE 600 arrangements can be made.
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