the incredibly hard k****r problems

Six cards problem:

There are C(6,3) = 20 ways to distribute the cards to the couples. For each of these ways, there is one way to distribute the cards within each couple so that both people have the same card number. Therefore, there are 20 ways to distribute the cards so that both people in each couple have the same card number. The total number of ways to distribute the cards is C(9,6) = 84, so the probability is 20/84​ = 5/21​​.

sorry, but that is wrong

I may have tried to help but the writing is too small.  

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