Let A, B 2 subsets of the set {1,2,...,n}, The number of elements of A, and the number of elements of B are r (|A| = |B| = r), 1 <= r <= n. What is the probability that exactly k elements are in A and B, with k in {0,1,...r} ?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Let A, B 2 subsets of the set {1,2,...,n}, The number of elements of A, and the number of elements of B are r (|A| = |B| = r), 1 <= r <= n. What is the probability that exactly k elements are in A and B, with k in {0,1,...r} ?

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From the given information, the set is {1, 2,……..,n}. The two subsets are A and B.

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