If ^nC_9=^nC_3 , what is n?

The correct answer is Option (3) → 12

Choosing \(r\) things out of \(n\) is the same as leaving out the other \(n-r\), so \({^nC}_r={^nC}_{n-r}\). Hence if \({^nC}_a={^nC}_b\) with \(a\ne b\), then \(a+b=n\).

• Here the two lower numbers are 9 and 3, so \(n=9+3=12\).