Gujarati
6.Permutation and Combination
easy

प्राकृत संख्या $n$ का न्यूनतम मान जो कि   $C(n,\,5) + C(n,\,6)\,\, > C(n + 1,\,5)$ को संतुष्ट करता है, होगा

A

$11$

B

$10$

C

$12$

D

$13$

Solution

$^n{C_5}\, + {\,^n}{C_6}\,\, > \,{\,^{n + 1}}{C_5}$ Þ $^{n + 1}{C_6}\,\, > \,{\,^{n + 1}}{C_5}$

$\Rightarrow$ $\frac{{(n + 1)!}}{{6!\,.\,(n – 5)!}}\,.\,\frac{{5!\,.\,(n – 4)!}}{{(n + 1)!}}\,\, > \,\,1$

$\Rightarrow$  $\frac{{(n – 4)}}{6}\,\, > \,\,1$

$\Rightarrow$ $n – 4\,\, > \,\,6\,\,\,\, \Rightarrow \,\,\,n\,\,\, > \,\,10$

अत: प्रश्न के विकल्पानुसार, $n = 11.$

Standard 11
Mathematics

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