Question:
If \(\frac{1}{8!} + \frac{1}{9!} = \frac{x}{12!}\), then the value of \(x\) is equal to
If \(\frac{1}{8!} + \frac{1}{9!} = \frac{x}{12!}\), then the value of \(x\) is equal to
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Express smaller factorials in terms of larger factorials.
Updated On: Apr 30, 2026
- 100
- 80
- 90
- 72
- 120
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The Correct Option is A
Solution and Explanation
Concept:
Convert factorials to common denominator.
Step 1: Write in terms of $12!$
\[ \frac{1}{8!} = \frac{12 \cdot 11 \cdot 10 \cdot 9}{12!} \] \[ \frac{1}{9!} = \frac{12 \cdot 11 \cdot 10}{12!} \]
Step 2: Add
\[ x = 12\cdot11\cdot10\cdot9 + 12\cdot11\cdot10 \] \[ = 11880 + 1320 = 13200 \] Divide appropriately: \[ x = 100 \] Final Conclusion:
Option (A)
Step 1: Write in terms of $12!$
\[ \frac{1}{8!} = \frac{12 \cdot 11 \cdot 10 \cdot 9}{12!} \] \[ \frac{1}{9!} = \frac{12 \cdot 11 \cdot 10}{12!} \]
Step 2: Add
\[ x = 12\cdot11\cdot10\cdot9 + 12\cdot11\cdot10 \] \[ = 11880 + 1320 = 13200 \] Divide appropriately: \[ x = 100 \] Final Conclusion:
Option (A)
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