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For \(0\le r\le n\), which of the following identities represents the symmetry property of combinations?जहाँ \(0\le r\le n\), निम्नलिखित में से कौन-सी पहचान संयोजनों की सममिति (symmetry) का गुण दर्शाती है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\binom{n}{r}=\binom{n}{n-r}\)\(\binom{n}{r}=\binom{n}{n-r}\)
Choosing \(r\) objects from \(n\) is equivalent to deciding which \(n-r\) objects are left out; hence \(\binom{n}{r}=\binom{n}{n-r}\). Option D is Pascal’s identity, not symmetry. Exam tip: use complementary selection to spot this relation quickly.\(\binom{n}{r}\) वस्तुओं में से \(r\) चुनना उतना ही है जितना \(n-r\) वस्तुओं को छोड़ना, इसलिए \(\binom{n}{r}=\binom{n}{n-r}\)। विकल्प D पास्कल की पहचान है, सममिति नहीं। परीक्षा में पूरक चयन का विचार याद रखें।
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