Combination of \(r\) objects chosen from \(n\) distinct objects for JEE

Formula

\[{}^nC_r=\frac{n!}{r!(n-r)!}\]

Variables: \(n\) is total number of distinct objects, \(r\) is number selected.

Conditions: \(0\le r\le n\), \(n,r\in \mathbb{Z}_{\ge 0}\).

Unordered selections, committee formation, choosing groups.