\(^{5y}{C}_2\) = 190, find the value of y

Assessment: WAEC SSCE - Further Mathematics - 2021 (Essay) Subject: Further Mathematics

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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.)

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