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Find X in Each of the Following: 1 6 ! + 1 7 ! = X 8 ! - Mathematics

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Find x in each of the following:

\[\frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!}\]
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Solution

\[\frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!}\]
\[ \Rightarrow \frac{1}{6!} + \frac{1}{7(6!)} = \frac{x}{8!}\]
\[ \Rightarrow \frac{7 + 1}{7(6!)} = \frac{x}{8!}\]
\[ \Rightarrow \frac{8}{7!} = \frac{x}{8!}\]
\[ \Rightarrow \frac{8}{7!} = \frac{x}{8 \times 7!}\]
\[ \Rightarrow x = 64\]

Concept: Permutations
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Exercise 16.1 | Q 3.3 | Page 4

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