Prove that $\gcd({n \choose i},{n \choose j})>1,~1<i,j<n$

Prove that $\gcd({n \choose i},{n \choose j})>1,~0<i,j<n$

My work:
I tried expanding $n \choose i$ and $n \choose j$ to find that there is some number that divides both and after division the numbers are still integers, but I could not prove that they are integers. Please help.

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