Explain/solve the Matching Problem in the simplest terms

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Explain/solve the "Matching Problem" in the simplest terms

How would you explain and solve the "Matching Problem" to a HS math club? give the simplest explanation and solution you know.
 
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You mean the stable matching problem, from graph theory?
 


matching problem like the classic: "An absent-minded secretary prepares n letters and envelopes to send to n different people, but then randomly stuffs the letters into the envelopes. A match occurs if a letter is inserted in the proper envelope. Find the probability a match happens."
 
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There are many different problems involving matching one set against another.
 


redphoton said:
matching problem like the classic: "An absent-minded secretary prepares n letters and envelopes to send to n different people, but then randomly stuffs the letters into the envelopes. A match occurs if a letter is inserted in the proper envelope. Find the probability a match happens."

If P is the probability that a match DOESN'T happen, then 1-P is the probability that a match happens. Is this what you want?
 

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