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Unique combinations in a set.(+)

by Solumsen
Tags: combinations, unique
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Jan21-14, 06:33 AM
P: 1
Hey there!

I will start of with saying Im not very good at English when considering mathematical
terms, neither an expert in Math.

My question goes as this:

I have a set of 1000 questions - which will be given in rounds with a set of 10.
So every round, you get 10 questions out of the 1000.

We want to change out 5 questions in every round.
So we want to have not only to have the total number of combinations
where 1 question is unique - but where a set of 5 is.

Please, if the formulation is a bit misleading - i will try to clarify in a reply.
As i said, this is even hard for me to question in the right way!

- Thanks in advance
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Jan21-14, 06:38 AM
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tiny-tim's Avatar
P: 26,160
Hey Solumsen! Welcome to PF!

I don't understand

you want 10 questions, each of which has not been asked before

but that automatically means that any 5 of them will not have been asked before
Jan21-14, 08:21 AM
P: 540
The number of unique sets of 5 would be 1000!/(5!*995!).
The number of unique sets of 10 would be 1000!/(10!*990!).
The number of unique ways of grouping all unique sets of 10 into two groups of 5 would be (10!/(2*5!*5!))(1000!/(10!*990!)).

Since I can't quite figure out what the problem is, I don't know if any of this helps.

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