Identity using a combinatorial proof

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Reference no: EM13322781

Let n and k be integers with n ≥ k + 2 and k ≥ 2. Prove the following identity using a combinatorial proof:
(n choose k) = ((n - 2) choose k) + 2 . ((n - 2) choose(k - 1)) + ((n - 2) choose (k - 2)).

Reference no: EM13322781

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