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What is the value of (\binom{15}{7}-\binom{14}{7})?(\binom{15}{7}-\binom{14}{7}) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 30033003
Using Pascal’s identity, \(\binom{n}{r}-\binom{n-1}{r}=\binom{n-1}{r-1}\). Therefore, \(\binom{15}{7}-\binom{14}{7}=\binom{14}{6}=3003\). The value 3432 is \(\binom{14}{7}\), not the required difference. Exam tip: Use Pascal’s identity for such differences instead of expanding factorials.पास्कल के सर्वसमिका के अनुसार \(\binom{n}{r}-\binom{n-1}{r}=\binom{n-1}{r-1}\)। अतः \(\binom{15}{7}-\binom{14}{7}=\binom{14}{6}=3003\)। विकल्प 3432, \(\binom{14}{7}\) का मान है, अंतर का नहीं। परीक्षा टिप: ऐसे अंतर में पास्कल की सर्वसमिका लगाकर लंबी गणना से बचें।
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