Question

найти n, если...
$a \binom{2}{n} \times c \binom{n-1}{n} = 48$
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Answer 1

Ответ:

Формулы:    $A_{n}^{k}=n\cdt (n-1)\cdot ...\cdot (n-k+1)\ \ ,\ \ C_{n}^{k}=\dfrac{A_{n}^{k}}{k!}\ \ ,\ \ C_{n}^{k}=C_{n}^{\, n-k}$   .  

$A_{n}^2\cdot C_{n}^{n-1}=48n^2\\\\n\cdot (n-1)\cdot C_{n}^{n-(n-1)}=48n^2\\\\n\cdot (n-1)\cdot C_{n}^1=48n^2\\\\n\cdot (n-1)\cdot n=48n^2\\\\n^2\cdot (n-1)=48n^2\\\\n-1=48\\\\n=49\in \mathbb{N}\\\\Otvet:\ n=49\ .$