3. Let n be a positive integer and let k be an integer satisfying 0 ≤ k < n. (a) Explain what the Stirling numbers S(n, k) count. (b) Prove the formula S(n, k) = S(n − 1, k − 1) + kS(n − 1, k). 1 (c) With A = {1,2,3,4}, write down all distributions of elements of A into 2 unlabelled cells (allowing cells to be empty).

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