Point Picker II

EasyProbability

Fix $1 \leq r \leq n$ such that $2r \leq n$ . Andy and Barry are selecting uniformly random $r-$ element subsets from $[n] = \{1,2,\dots,n\}$ . Find the probability that Andy and Barry select disjoint subsets when $r = 4$ and $n = 10$ .

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