Category: Permutation and Combination

Question Number 43824 by Necxx last updated on 15/Sep/18 Answered by MJS last updated on 16/Sep/18 $$\left(\frac{1}{2}\right)!=\frac{\sqrt{\pi }}{2}$$$$\left(\frac{1}{2}\right)!+\left(\frac{1}{2}\right)!=\sqrt{\pi }$$$$\left(\mathrm{A}\right)1!=1$$$$\left(\mathrm{B}\right)\sin 45°=\frac{\sqrt{2}}{2}$$$$\left(\mathrm{C}\right)\:\:\sqrt{\mathrm{arccos}\:−\mathrm{1}}=\sqrt{\pi}…

Question Number 43659 by Joel578 last updated on 13/Sep/18 $$\mathrm{An}\mathrm{unfair}\mathrm{coin}\mathrm{with}\mathrm{the}\mathrm{probability}\mathrm{of}\mathrm{getting}$$$$\mathrm{head}\mathrm{in}\mathrm{one}\mathrm{toss}=\frac{1}{5}.$$$$\mathrm{If}\mathrm{coin}\mathrm{tosses}n\mathrm{times},\mathrm{the}\mathrm{probability}\mathrm{of}$$$$\mathrm{getting}2\mathrm{heads}\mathrm{is}\mathrm{equal}\mathrm{to}\mathrm{the}\mathrm{probability}\mathrm{of}$$$$\mathrm{getting}3\mathrm{heads}.\mathrm{Find}n$$ Commented by math1967 last updated…

Question Number 108638 by bemath last updated on 18/Aug/20 $$\frac{bemath}{★}$$$$provethat\left(\begin{array}{c}n-1\\ r\end{array}\right)+\left(\begin{array}{c}n-1\\ r-1\end{array}\right)=\left(\begin{array}{c}n\\ r\end{array}\right)$$ Answered by bemath last updated on 18/Aug/20 Terms of Service Privacy…

Question Number 108450 by bemath last updated on 17/Aug/20 $$\frac{\mathcal{B}e\mathcal{M}ath}{\subset \supset }$$$$\left(1\right)find\left(\frac{1}{2}\right)!$$$$\left(2\right)\underset{0}{\stackrel{\pi /2}{\int }}\frac{x\sin x}{{(1+\cos x)}^2}dx$$ Commented by Smail last updated on…

Question Number 173975 by savitar last updated on 22/Jul/22 $$$$$$$$$$$$$$\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{{y}^{{a}−\mathrm{1}} }{\left(\mathrm{1}+{y}\right)^{{b}} }\:{dy}\:\overset{{u}=\frac{\mathrm{1}}{\mathrm{1}+{y}}} {=}\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left(\mathrm{1}−{u}\right)^{{a}−\mathrm{1}} }{{u}^{{a}−\mathrm{1}} }\:{u}^{{b}}…