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?
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.