Prove by induction that the number of (unordered) pairs of integers between 0 and (n-1) is (n(n-1)

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Prove by induction that the number of (unordered) pairs of integers between 0 and \(n-1\) is \(n(n-1) / 2\), and then prove by induction that the number of (unordered) triples of integers between 0 and \(n-1\) is \(n(n-1)(n-2) / 6\).

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