Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

I have two problems, probably easy, but I can't get it solved or at least find a solution based on some bulletproof idea :)

Problem 1

A host makes a party for his friends every day. To the party three guests are always invited. How many ways can the host invite his 7 friends, so that all the friends will be invited within a week?

Problem 2

Let's haven = 3kpeople andktables, each for three people. How many times is it neccessary to seat the people to the tables, so that each one pair will meet at exactly one seating? Can it be done for even number of tables? (Find general expression for tables withsplaces andtpeople who should meet exactly once.

To the first problem, I only found out (don't know if correctly), that each one has to be invited twice (to meet each other), but I don't know how to combine it. As a result, I got some this strange one:

[tex]

\left( \begin{array}{c} 7 \\ 3 \end{array} \right)^7

[/tex]

And for the second one I got (using experimental method)

[tex]

\frac{n}{3} + 1

[/tex]

Could someone explain these problems to me please?

Thank you.

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# Two combinatorial problems

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