[tex]\displaystyle\bf\\C_{8} ^{3} =\frac{8!}{3!\cdot(8-3)!} =\frac{5!\cdot6\cdot 7\cdot 8}{1\cdot 2\cdot 3\cdot5!} =7\cdot 8=56\\\\\\P_{6} =6!=1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6\\\\\\A_{7} ^{4} =\frac{7!}{(7-4)!} =\frac{7!}{3!} =\frac{3!\cdot4\cdot5\cdot6\cdot 7}{3!}=4\cdot 5\cdot 6\cdot 7 \\\\\\\frac{C_{8} ^{3} \cdot P_{6} }{A_{7} ^{4} } =\frac{56\cdot1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6 }{4\cdot 5\cdot 6\cdot 7} =8\cdot6=48[/tex]