Question: Let A1, A2, . . ., An be a collection of sets, where A1 = A2 = ..... = An and | At | =

Let A1, A2, . . ., An be a collection of sets, where A1 = A2 = ..... = An and | At | = k > 0 for all 1 < i < n. (a) Prove that the given collection has a system of distinct representatives if and only if n < k. (b) When n < k, how many different systems exist for the collection?

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