Question 1 Report
\(^{5y}{C}_2\) = 190, find the value of y
Use \({}^{n}C_{2}=\dfrac{n(n-1)}{2}\) with \(n=5y\):
\[{}^{5y}C_{2}=\frac{5y(5y-1)}{2}=190\]
So \(5y(5y-1)=380\). Let \(n=5y\):
\[n^{2}-n-380=0\Rightarrow n=\frac{1\pm\sqrt{1+1520}}{2}=\frac{1\pm39}{2}\]
Taking the positive root, \(n=20\). Since \(n=5y\):
\[5y=20\Rightarrow \boxed{y=4}\]
(The negative root \(n=-19\) is rejected.)
Answer Details
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