Question

помогите пожалуйста ​

Answer 1

$1) \ \dfrac{P_{8} -P_{6} }{P_{5} } =\dfrac{8!-6!}{5!} =\dfrac{5!(3!-6)}{5!} =3!-6=1\cdot 2\cdot 3-6=6-6=\boxed0\\\\\\2) \ A_{8} ^{3} =\dfrac{8!}{(8-3)!} =\dfrac{8!}{5!}=\dfrac{5!\cdot 6\cdot 7\cdot 8}{5!} =6\cdot 7\cdot 8\\\\\\A_{7} ^{2}=\dfrac{7!}{(7-2)!} =\dfrac{7!}{5!}=\dfrac{5!\cdot 6 \cdot 7}{5!} =6\cdot 7\\\\\\C_{7} ^{4}=\dfrac{7!}{4!(7-4)!} =\dfrac{4!\cdot5\cdot 6\cdot 7}{4!\cdot3!} =\dfrac{5\cdot 6\cdot 7}{1\cdot 2\cdot 3} =5\cdot 7$

$\dfrac{A_{8} ^{3} -A_{7} ^{2} }{C_{7} ^{4} } =\dfrac{6\cdot 7\cdot 8-6\cdot 7}{5\cdot7} =\dfrac{6\cdot 7\cdot(8-1)}{5\cdot7} =\dfrac{6\cdot 7}{5}=\boxed{8,4}$