[tex]\displaystyle\bf\\1)\\\\\frac{P_{7} }{P_{8} } \cdot A_{6} ^{4} =\frac{7!}{8!} \cdot \frac{6!}{(6-4)!} =\frac{7!}{7!\cdot 8} \cdot\frac{6!}{2!} =\frac{1}{8} \cdot \frac{2!\cdot 3\cdot 4\cdot 5\cdot 6}{2!} =3\cdot 5\cdot 3=45\\\\\\2)\\\\C_{6} ^{3} \cdot A_{3} ^{2} =\frac{6!}{3!\cdot(6-3)!} \cdot\frac{3!}{(3-2)!} =\frac{6!}{3!} =\frac{3!\cdot 4\cdot 5\cdot 6}{3!} =4\cdot 5\cdot 6=120[/tex]