Key factorial identities: n! = n * (n-1)!, 0! = 1 (by convention, for nCn = 1 to hold). For simplification: n!/(n-2)! = n(n-1), n!/(n-3)! = n(n-1)(n-2). Never compute large factorials directly — always cancel. Example: 20!/(18! * 2!) = $\frac{20 * 19}{2}$ = 190. In JEE numerical answers, express nCr using the smaller of r and n-r.