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What is the value of \(\frac{10!}{6!,4!}+\frac{10!}{7!,3!}\)?\(\frac{10!}{6!,4!}+\frac{10!}{7!,3!}\) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 330330
\(\frac{10!}{6!\,4!}=\binom{10}{4}=210\) and \(\frac{10!}{7!\,3!}=\binom{10}{3}=120\). Therefore, their sum is \(210+120=330\), so option D is correct. Exam tip: Recognising expressions of the form \(\frac{n!}{r!(n-r)!}\) as combinations makes calculation quicker.\(\frac{10!}{6!\,4!}=\binom{10}{4}=210\) तथा \(\frac{10!}{7!\,3!}=\binom{10}{3}=120\) है। अतः योग \(210+120=330\) होगा। इसलिए सही विकल्प D है। परीक्षा टिप: ऐसे व्यंजकों को \(\binom{n}{r}\) के रूप में पहचानने से गणना तेज होती है।
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