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(\binom{8}{5}) is equal to which expression?(\binom{8}{5}) किसके बराबर है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\binom{8}{3}\)\(\binom{8}{3}\)
Combinations follow the symmetry property \(\binom{n}{r}=\binom{n}{n-r}\). Therefore, \(\binom{8}{5}=\binom{8}{8-5}=\binom{8}{3}\), so option B is correct. In \(\binom{8}{2}\), the complementary selection is 6, not 5. Exam tip: Rewrite \(\binom{n}{r}\) as \(\binom{n}{n-r}\) to match such options quickly.संयोजन का सममिति गुण है: \(\binom{n}{r}=\binom{n}{n-r}\)। अतः \(\binom{8}{5}=\binom{8}{8-5}=\binom{8}{3}\), इसलिए विकल्प B सही है। \(\binom{8}{2}\) में पूरक संख्या 6 होती है, 5 नहीं। परीक्षा टिप: \(\binom{n}{r}\) को तुरंत \(\binom{n}{n-r}\) में बदलकर विकल्पों से मिलाइए।
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