Question
Download Solution PDFयदि 2nC3 : nC2 = 12 : 1 है, तो n का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
एक समय (r ≤ n) में r लिए गए n विशिष्ट वस्तुओं के सभी संयोजनों की संख्या निम्न है:
\(^{n}C_{r}=\frac{n!}{(n-r)!r!}\)
गणना:
चूँकि 2nC3 : nC2 = 12 : 1
\(⇒ \frac{2n!}{(2n-3)!\space 3!}:\frac{n!}{(n-2)!\space 2!}=12:1\)
\(⇒ \frac{2n(2n-1)(2n-2)}{3\times 2\times 1}:\frac{n(n-1)}{2\times 1}=12:1\)
⇒ 2n - 1 = 9
⇒ n = 5
Last updated on May 31, 2025
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