JEE Advance - Mathematics (2000 - No. 18)
For $$2 \le r \le n,\,\,\,\,\left( {\matrix{
n \cr
r \cr
} } \right) + 2\left( {\matrix{
n \cr
{r - 1} \cr
} } \right) + \left( {\matrix{
n \cr
{r - 2} \cr
} } \right) = $$
$$\left( {\matrix{
{n + 1} \cr
{r - 1} \cr
} } \right)$$
$$2\left( {\matrix{
{n + 1} \cr
{r + 1} \cr
} } \right)$$
$$2\left( {\matrix{
{n + 2} \cr
r \cr
} } \right)$$
$$\left( {\matrix{
{n + 2} \cr
r \cr
} } \right)$$