Question:
If \(\frac{1}{6!}+\frac{1}{7!}=\frac{x}{8!}\), find x.
If \(\frac{1}{6!}+\frac{1}{7!}=\frac{x}{8!}\), find x.
Updated On: Oct 21, 2023
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Solution and Explanation
Given, \(\frac{1}{6!}+\frac{1}{7!}=\frac{x}{8!}\)
\(⇒\frac{1}{6!}+\frac{1}{7\times6!}=\frac{x}{8\times7\times6!}\)
\(⇒\frac{1}{6!}(1+\frac{1}{7})=\frac{x}{8\times7\times6!}\)
\(⇒1+\frac{1}{7}=\frac{x}{8\times7}\)
\(⇒\frac{8}{7}=\frac{x}{8\times7}\)
\(⇒x=\frac{8\times8\times7}{7}\)
\(∴x=64\)
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Permutations and Combinations
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