Question: this is a combinatorial analysis question, which is course MATH 3343 question. please help () Suppose a roommate assignment 3 an assignment of 2n men

this is a combinatorial analysis question, which is course MATH 3343 question. please help

() Suppose a roommate assignment 3 an assignment of 2n men into n rooms S. T. every room is assigned exactly 2 men, A roommate assignment is unstable if there is Two men who are not roommates but prefer each other over their current one, otherwise, it is stable, Is it true that there exist a stable roommate assignment? If ges, use an algorithm to realize it. If no find a counter example

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