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Let $A = \{1\dots n\}$. Do partition of set $A$ on pairwise disjoint two- and three-element subsets randomly. For each n determine probability that number of two-element subsets is equal to three-element subsets.

I don't clearly understand with what i can start to solve it. I only know about Bell's numbers and I guess there are some formula only for $n$ witch could be determine in term of integers $3a + 5b = n$. Can you help me to solve this problem or give me advice how to to do this?

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Use the binomial coefficient to calculate the number of subset made from A, in particular $\binom{n-1}{k-1}$. Then it’s easy to compute the probability.

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