If Combination of $n$ choose $k$ $n\choose k$ and combination of $a$ choose $b$ $a\choose b$ are equal does that imply that $n=a$ and $k=b$ or $k=a-b$? Or are there other posibilities?
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Some counterexamples: $\binom{n}{0} = \binom{n}{n} = 1$; $\binom{n}{k} = \binom{n}{n-k}$; $\binom{4}{2} = \binom{6}{1} = 6$. – Ertxiem - reinstate Monica Apr 25 '19 at 17:22
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Hint: What is ${n\choose 1}$ equal to? Hence, what is $${{n \choose k} \choose 1}$$ equal too?
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