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Prove by induction that the number of 2-subsets of an n-set

**A**equals**n(n-1)/2**.You are using an out of date browser. It may not display this or other websites correctly.

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- Thread starter Ella087
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Prove by induction that the number of 2-subsets of an n-set **A** equals **n(n-1)/2**.

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Say the 2-set is A= {1,2} and the three set is B={1,2,3}. A 2-subset of A is certainly also a 2-subset of B, so you have {1,2}, but there are more 2-subsets of B, those containing 3. What can you pair 3 with? Apparently with any of the elements of A, which gives you another two 2-subsets of B, namely {1,3},{2,3}.

So in total there are three 2-subsets of a set B with three elements, in agreement with your formula.

Can you generalize this?

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mathman

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