16!+17! = x8! ⇒ 8![16!+17!] = x ⇒8!6!+8!7! = x ⇒8 × 7 × 6!6! + 8 × 7!7! = x ⇒ 8 × 7 + 8 = x ⇒ 56 + 8 = x ⇒ x = 64 ...

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Byju's Answer

Standard XII

Mathematics

Combination with Restrictions

If 16!+17!=x8...

Question

If $\frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!},$ find $x .$

Name: NCERT - Grade 11 - Mathematics - Permutations and Combinations - Q18
Uploaded: 2022-07-04T10:36:42+05:30
Description: 16!+17! = x8! ⇒ 8![16!+17!] = x ⇒8!6!+8!7! = x ⇒8 × 7 × 6!6! + 8 × 7!7! = x ⇒ 8 × 7 + 8 = x ⇒ 56 + 8 = x ⇒ x = 64 ...

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Solution

$\frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!}$
$\Rightarrow 8! [\frac{1}{6!} + \frac{1}{7!}] = x$
$\Rightarrow \frac{8!}{6!} + \frac{8!}{7!} = x$
$\Rightarrow \frac{8 \times 7 \times 6!}{6!} + \frac{8 \times 7!}{7!} = x$
$\Rightarrow 8 \times 7 + 8 = x$
$\Rightarrow 56 + 8 = x$
$\Rightarrow x = 64$

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