$a\text{)}\left(\begin{array}{c}6\\ 3\end{array}\right)=\frac{6!}{\left(6-3\right)!\cdot 3!}=\frac{3!\cdot 4\cdot 5\cdot 6}{3!\cdot 3!}=$   

$=\frac{4\cdot 5\cdot 6}{3!}=\frac{4\cdot 5\cdot 6}{6}=4\cdot 5=20$  

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$b\text{)}2\cdot \left(\begin{array}{c}7\\ 5\end{array}\right)=2\cdot \frac{7!}{\left(7-5\right)!\cdot 5!}=2\cdot \frac{5!\cdot 6\cdot 7}{2!\cdot 5!}=$  

$=2\cdot \frac{6\cdot 7}{2}=6\cdot 7=42$  

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$c\text{)}\left(\begin{array}{c}8\\ 2\end{array}\right)-\left(\begin{array}{c}5\\ 3\end{array}\right)=\frac{8!}{\left(8-2\right)!\cdot 2!}-\frac{5!}{\left(5-3\right)!\cdot 3!}=$  

$=\frac{6!\cdot 7\cdot 8}{6!\cdot 2!}-\frac{3!\cdot 4\cdot 5}{2!\cdot 3!}=\frac{7\cdot 8}{2}-\frac{4\cdot 5}{2}=$  

$=7\cdot 4-2\cdot 5=28-10=18$  

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$d\text{)}\left(\begin{array}{c}10\\ 9\end{array}\right)\cdot \left(\begin{array}{c}9\\ 0\end{array}\right)=\frac{10!}{\left(10-9\right)!\cdot 9!}\cdot \frac{9!}{\left(9-0\right)!\cdot 0!}=$  

$=\frac{9!\cdot 10}{1!\cdot 9!}\cdot \frac{9!}{9!}=10\cdot 1=10$  

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$e\text{)}\left(\begin{array}{c}8\\ 5\end{array}\right)\cdot 3!=\frac{8!}{\left(8-5\right)!\cdot 5!}\cdot 3!=$  

$=\frac{5!\cdot 6\cdot 7\cdot 8}{3!\cdot 5!}\cdot 3!=\frac{6\cdot 7\cdot 8}{6}\cdot 6=6\cdot 7\cdot 8=336$  

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$f\text{)}\left(\begin{array}{c}9\\ 4\end{array}\right)-4!=\frac{9!}{\left(9-4\right)!\cdot 4!}-4!=$  

$=\frac{5!\cdot 6\cdot 7\cdot 8\cdot 9}{5!\cdot 4!}-4!=\frac{6\cdot 7\cdot 8\cdot 9}{4!}-4!=$  

$=\frac{6\cdot 7\cdot 8\cdot 9}{24}-24=\left(7\cdot 2\cdot 9\right)-24=126-24=102$