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What is the value of (\binom{10}{4}-\binom{9}{4})?(\binom{10}{4}-\binom{9}{4}) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 8484
Using Pascal’s identity, \(\binom{n}{r}-\binom{n-1}{r}=\binom{n-1}{r-1}\), we get \(\binom{10}{4}-\binom{9}{4}=\binom{9}{3}=84\). Hence, the correct answer is 84. The value 126 is \(\binom{9}{4}\), not the required difference. Exam tip: Recognising Pascal’s identity avoids lengthy calculation in such questions.पास्कल के सर्वसमिका
\(\binom{n}{r}-\binom{n-1}{r}=\binom{n-1}{r-1}\) के अनुसार, \(\binom{10}{4}-\binom{9}{4}=\binom{9}{3}=84\)। अतः सही उत्तर 84 है। \(126\), \(\binom{9}{4}\) का मान है, अंतर का नहीं। परीक्षा टिप: ऐसे घटाव में पहले पास्कल सर्वसमिका पहचानने से लंबी गणना बचती है।
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