Permutations and Combinations HElp please Math Statistics

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Leah.J
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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?

I know 6P5 and I know there's 1 last period that any of the 5 subjects can take but I don't know how to include it in the calculation
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SkyRunner61
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Your calculation shouldn’t actually include 6P5, because it denotes the number of ways of choosing 5 of 6 items where the order does matter. The items here aren’t the number of periods, but rather the number of subjects that you can choose from, which is 5.

Next, you identified that the other remaining period can be one of 5 subjects, so we multiply our permute number by 5. However, this bonus period of one of the subjects doesn’t have to be the last one, does it? It could be any of the periods, so what do we have to multiply by?

You also have to think about having two consecutive periods of the same class.
Last edited by SkyRunner61; 1 year ago
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