If 18-19-x10- find x-

Name: NCERT - Grade 11 - Mathematics - Permutations and Combinations - Q14
Uploaded: 2022-07-04T10:36:42+05:30
Description: Simplification, 18!+19!=x10! ⇒ 10![18!+19!]=x ⇒10!8!+10!9!=x ⇒10× 9× 8!8!+10× 9!9!=x ⇒ 90+10=x ∴ x=100 ...

Simplification, 18!+19!=x10! ⇒ 10![18!+19!]=x ⇒10!8!+10!9!=x ⇒10× 9× 8!8!+10× 9!9!=x ⇒ 90+10=x ∴ x=100 ...

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Byju's Answer

Standard XII

Mathematics

Combination with Restrictions

If 18!+19!=x1...

Question

If $\frac{1}{8!} + \frac{1}{9!} = \frac{x}{10!},$ find $x .$

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Solution

Simplification,
$\frac{1}{8!} + \frac{1}{9!} = \frac{x}{10!}$
$\Rightarrow 10! [\frac{1}{8!} + \frac{1}{9!}] = x$
$\Rightarrow \frac{10!}{8!} + \frac{10!}{9!} = x$
$\Rightarrow \frac{10 \times 9 \times 8!}{8!} + \frac{10 \times 9!}{9!} = x$
$\Rightarrow 90 + 10 = x$
$∴ x = 100$

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