Unique combinations in a set.(+)

  1. Hey there!

    I will start of with saying I´m 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
  2. jcsd
  3. tiny-tim

    tiny-tim 26,016
    Science Advisor
    Homework Helper

    Hey Solumsen! Welcome to PF! :smile:

    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 :confused:
  4. 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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