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# Inclusion-Exclusion! Watch

1. Hi guys,

Question is above. Part a was fine.

Now for part b, they want us to find the number of sets in B, that is |B|. But B isn't a union or intersection of the subsets, it's simply a collection of all subsets - how do we use the inclusion exclusion principle here? What are we taking the union off?

I always find these questions quite difficult - any help is appreciated!

Thanks.
2. (Original post by hmark101)
Now for part b, they want us to find the number of sets in B, that is |B|. But B isn't a union or intersection of the subsets, it's simply a collection of all subsets - how do we use the inclusion exclusion principle here? What are we taking the union off?

I always find these questions quite difficult - any help is appreciated!

Thanks.
The clue, to me, is the statement "there is at least one i such that". So there, could be 1, or 2, or 3,...

So, how many B's are there such that , and then the rest of the . Then you need to remove the double counted ones - see the inclusion/exclusion arising?
3. (Original post by ghostwalker)
The clue, to me, is the statement "there is at least one i such that". So there, could be 1, or 2, or 3,...

So, how many B's are there such that , and then the rest of the . Then you need to remove the double counted ones - see the inclusion/exclusion arising?
Right... I sort of see where this is going.

Ok, so there are (n choose k) B's that satisfy condition (i) - that is, the size of a subset B must be k.

But we also need to satisfy condition (ii). This is the trouble I am having... how do we know how many satisfy (ii)?!
4. (Original post by hmark101)
Right... I sort of see where this is going.
Any selection of k elements will satisfy condition 1. It's condition 2 that my previous post was trying to get you to focus one.
5. (Original post by ghostwalker)
Any selection of k elements will satisfy condition 1. It's condition 2 that my previous post was trying to get you to focus one.
Yes - I understand. The trouble I am having is: how do we know how many B's there are that satisfy condition 2? I can't seem to work that out.
6. (Original post by hmark101)
Yes - I understand. The trouble I am having is: how do we know how many B's there are that satisfy condition 2? I can't seem to work that out.
This is where your inclusion/exclusion comes in.

As I said in my first post, start by considering how many B's exist such that |A1nB|=3

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