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perms and combs

I have never got to grips with this topic and with time on my hands decided to try again. This is a particular question that I cannot understand at all.

An art collector who owns 10 original paintings is preparing a will. In how many ways may the collector leave these paintings to three heirs.

I can't even think what it might mean. Could heir 1 get them all or heir 1 get 9 and heir 2 get one and so on?

Can someone please explain in English what I need to think. I have the answer - it's 3^15 but I just can't work out why.

Thanks
Original post by maggiehodgson
I have never got to grips with this topic and with time on my hands decided to try again. This is a particular question that I cannot understand at all.

An art collector who owns 10 original paintings is preparing a will. In how many ways may the collector leave these paintings to three heirs.

I can't even think what it might mean. Could heir 1 get them all or heir 1 get 9 and heir 2 get one and so on?

Can someone please explain in English what I need to think. I have the answer - it's 3^15 but I just can't work out why.

Thanks


Well, he can give painting 1 to heir 1, 2, or 3. Then he can give painting 2 to heir 1, 2, or 3, then he can give painting 3 to heir 1, 2, or 3 .... painting 10 to heir 1, 2, or 3.

Those are all independent choices, so I'd say that you'd get a branching tree of 3^10 leaves, which differs from your answer.
Original post by atsruser
Well, he can give painting 1 to heir 1, 2, or 3. Then he can give painting 2 to heir 1, 2, or 3, then he can give painting 3 to heir 1, 2, or 3 .... painting 10 to heir 1, 2, or 3.

Those are all independent choices, so I'd say that you'd get a branching tree of 3^10 leaves, which differs from your answer.


Thanks so much - it makes perfect sense. And yes I did get the wrong index it was 10 not 15.
Original post by maggiehodgson
Thanks so much - it makes perfect sense. And yes I did get the wrong index it was 10 not 15.


Good. I couldn't see where my argument went wrong.

These can be tricky to reason about, however, and they take practise. I'm not great at them. Take a look at the first two principles on this page as you will use them frequently in combinatorial problems:

https://en.wikipedia.org/wiki/Combinatorial_principles
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B_9710
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The title of the thread makes it seem like you're talking about hair.

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