Question

Решите уравнение по теме "Сочетание"
Нужно 1 и 2, пожалуйста. С подробным решением, срочно​

Answer 1

$1) \ C_{n} ^{2} =28\\\\\dfrac{n!}{2!\cdot(n-2)!} =28\\\\\\\dfrac{(n-2)!\cdot(n-1)\cdot n}{1\cdot2\cdot(n-2)!} =28\\\\\\n(n-1)=56\\\\\\n^{2}-n-56=0\\\\\\n_{1} =8\\\\\\n_{2} =-7<0-neyd\\\\\\Otvet:\boxed8$

$2) \ C_{n} ^{n-3} =20\\\\\\\dfrac{n!}{(n-3)!\cdot(n-n+3)!}}=20\\\\\\\dfrac{(n-3)!\cdot(n-2)\cdot (n-1)\cdot n}{(n-3)!\cdot 3!} =20\\\\\\\dfrac{n(n-1)(n-2)}{1\cdot 2\cdot 3}=20\\\\\\n(n-1)(n-2)=120\\\\\\n^{3} -3n^{2} +2n-120=0\\\\\\(n-6)(n^{2} +3n+20)=0\\\\\\Otvet:\boxed6$