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# Permutation and Combination watch

1. There are k different books and l copies of each in a college library. The number of ways in which a student can make a selection of one or more books is (l+1)^k-1. Can't prove it
2. (Original post by Spandy)
There are k different books and l copies of each in a college library. The number of ways in which a student can make a selection of one or more books is (l+1)^k-1. Can't prove it
It may help to work with a small example, say 2 books and 3 copies of each.

What does the formula come out as, and try listing all the options, may give you a clue as to how to proceed.
3. (Original post by ghostwalker)
It may help to work with a small example, say 2 books and 3 copies of each.

What does the formula come out as, and try listing all the options, may give you a clue as to how to proceed.
Thanks, but I was hoping for a more generalised approach
4. (Original post by Spandy)
Thanks, but I was hoping for a more generalised approach
Considering a small example is an excellent technique that allows you to explore a problem yourself.

Here is another approach, but to create it, I rely on a greater understanding of how the formula arose.

Consider one volume of which there are l copies, how many choices does the student have (allowing the fact that they might not take any)?

Similarly a second volume, ....

Etc.

Hence total number of choices, assuming they take at least one.

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Updated: January 20, 2015
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