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if-p-r-n-49-c-r-n-196-find-the-valve-of-r-and-n-pleas-sir-help-me-




Question Number 73983 by mhmd last updated on 17/Nov/19
if p_r ^n =49 , c_r ^n =196 find the valve of r and n?  pleas sir help me
$${if}\:{p}_{{r}} ^{{n}} =\mathrm{49}\:,\:{c}_{{r}} ^{{n}} =\mathrm{196}\:{find}\:{the}\:{valve}\:{of}\:{r}\:{and}\:{n}? \\ $$$${pleas}\:{sir}\:{help}\:{me} \\ $$
Answered by $@ty@m123 last updated on 17/Nov/19
4×^n P_r  =^n C_r   ⇒((4.n!)/((n−r)!))=((n!)/(r!(n−r)!))  ⇒ r!=(1/4)  Not possible.
$$\mathrm{4}×\:^{{n}} {P}_{{r}} \:=\:^{{n}} {C}_{{r}} \\ $$$$\Rightarrow\frac{\mathrm{4}.{n}!}{\left({n}−{r}\right)!}=\frac{{n}!}{{r}!\left({n}−{r}\right)!} \\ $$$$\Rightarrow\:{r}!=\frac{\mathrm{1}}{\mathrm{4}} \\ $$$${Not}\:{possible}. \\ $$
Commented by JDamian last updated on 17/Nov/19
^n P_r  <^n C_r ?  Why  4×?
$$\:^{{n}} {P}_{{r}} \:<\:^{{n}} {C}_{{r}} ? \\ $$$${Why}\:\:\mathrm{4}×? \\ $$
Commented by $@ty@m123 last updated on 17/Nov/19
∵ 4×49=196
$$\because\:\mathrm{4}×\mathrm{49}=\mathrm{196} \\ $$
Answered by arkanmath7@gmail.com last updated on 17/Nov/19
r! = (1/4)  search in gamma function  r! = Γ(r+1) = rΓ(r) = r∫_0 ^∞ e^(−x)  x^(r−1) dx
$${r}!\:=\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$${search}\:{in}\:{gamma}\:{function} \\ $$$${r}!\:=\:\Gamma\left({r}+\mathrm{1}\right)\:=\:{r}\Gamma\left({r}\right)\:=\:{r}\int_{\mathrm{0}} ^{\infty} {e}^{−{x}} \:{x}^{{r}−\mathrm{1}} {dx} \\ $$

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