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By how much is \( \frac{10!}{8!} \) greater than \( \frac{9!}{7!} \)?\( \frac{10!}{8!} \), \( \frac{9!}{7!} \) से कितना अधिक है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 1818
\(\frac{10!}{8!}=10\times9=90\), since \(8!\) cancels out. Similarly, \(\frac{9!}{7!}=9\times8=72\). Therefore, the required difference is \(90-72=18\). Option 16 may result from an error in multiplication or subtraction. Exam tip: expand factorials only up to the smaller factorial and cancel the common part.\(\frac{10!}{8!}=10\times9=90\), क्योंकि \(8!\) कट जाता है। इसी प्रकार \(\frac{9!}{7!}=9\times8=72\)। अतः अपेक्षित अंतर \(90-72=18\) है। विकल्प 16 तब मिलता है जब गुणनफल या घटाव में त्रुटि हो। परीक्षा टिप: भिन्नात्मक फैक्टोरियल में छोटे फैक्टोरियल तक विस्तार करके समान पदों को काटें।
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