Are the following statements true or false?

? True False  1. ${n \choose 2}{{n-2}\choose{k-2}} = {n \choose k} {k \choose 2}$

? True False  2. ${n \choose 0} - {n \choose 1} + {n \choose 2} + \cdots + (-1)^n {n \choose n} = 0$

? True False  3. $n! = (n-1)\big( (n-1)! + (n-2)!\big) \quad \text{ for } n \geq 2$

? True False  4. ${n \choose 0} + {n \choose 1} + {n \choose 2} + \cdots + {n \choose n} = n^2$

? True False  5. $D_n = (n-1)\big( D_{n-1} + D_{n-2}\big)$ where $D_n$ is the number of derangements of $n$ objects, and $n\geq 2$

? True False  6. ${n \choose k} = {n \choose {n-k}}$

? True False  7. $\sum_{k=0}^n 3^k {n \choose k} = 2^n$