Lembrando que $\left(\begin{array}{l}n\\ p\end{array}\right)=\frac{n!}{p!(n-p)!}$,

1. a) Calcule $\left(\begin{array}{l}6\\ 4\end{array}\right)$.
   

2. b) Simplifique a fração $\frac{\left(\begin{array}{l}12\\ 4\end{array}\right)}{\left(\begin{array}{l}12\\ 5\end{array}\right)}$
   

3. c) Determine os inteiros $n$ e $p$ de modo que $$\frac{\left(\begin{array}{l}n\\ p\end{array}\right)}{1}=\frac{\left(\begin{array}{c}n\\ p+1\end{array}\right)}{2}=\frac{\left(\begin{array}{c}n\\ p+2\end{array}\right)}{3}$$