Question

Проверьте равенства: а) С_n^6=(A_n^(n-6))/P_(n-6) ; б) С_15^6=C_15^9.

Answer 1

$\displaystyle\bf\\1)\\\\C_{n} ^{6} =\frac{A_{n}^{n-6} }{P_{n-6} } \\\\\\C_{n} ^{6} =\frac{n!}{6!\cdot(n-6)!} \\\\\\\frac{A_{n}^{n-6} }{P_{n-6} }=\frac{\frac{n!}{(n-n+6)!} }{(n-6)!} =\frac{\frac{n!}{6!} }{(n-6)!} =\frac{n!}{6!\cdot(n-6)!} \\\\\\Otvet \ : \ verno\\\\\\2)\\\\C_{15} ^{6} =C_{15} ^{9} \\\\\\\frac{15!}{6!\cdot(15-6)!} =\frac{15!}{9!\cdot(15-9)!}\\\\\\\frac{15!}{6!\cdot9!}=\frac{15!}{9!\cdot6!} \ \ - \ verno$