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What is the value of \(\frac{11!}{8!,3!}-\frac{9!}{7!,2!}\)?\(\frac{11!}{8!,3!}-\frac{9!}{7!,2!}\) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 129129
\(\frac{11!}{8!\,3!}=\frac{11\times10\times9}{3\times2\times1}=165\), and \(\frac{9!}{7!\,2!}=\frac{9\times8}{2\times1}=36\). Therefore, the required value is \(165-36=129\). A value such as \(126\) can result from simplifying the first term incorrectly. Exam tip: cancel common factorial parts first, then multiply the remaining factors.\(\frac{11!}{8!\,3!}=\frac{11\times10\times9}{3\times2\times1}=165\) तथा \(\frac{9!}{7!\,2!}=\frac{9\times8}{2\times1}=36\)। अतः आवश्यक मान \(165-36=129\) है। \(126\) जैसा विकल्प केवल पहला पद गलत सरल करने पर मिल सकता है। परीक्षा टिप: फैक्टोरियल को पहले समान पदों तक काटें, फिर शेष गुणन करें।
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