Equality of combinations

Question

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?

Answer 1

Hint: What is ${n\choose 1}$ equal to? Hence, what is $${{n \choose k} \choose 1}$$ equal too?