Category: Permutation and Combination

Question Number 67281 by Tony Lin last updated on 25/Aug/19 Commented by mr W last updated on 25/Aug/19 $$Iget3C_2^5+3C_2^5+12=72$$…

Question Number 1468 by havandip last updated on 11/Aug/15 $$$$ Answered by 123456 last updated on 11/Aug/15 $$\underset{x\to -\mathrm{\infty }}{\lim }f\left(x\right)=\mathrm{L}$$$$\mathrm{\forall }ϵ>0,\mathrm{\exists }\mathrm{M}\in \mathbb{R},\mathrm{\forall }x<\mathrm{M},\mid f\left(x\right)-\mathrm{L}\mid <ϵ$$…

Question Number 132382 by liberty last updated on 13/Feb/21 $$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{coefficient}{\mathrm{x}}^{10}$$$$\mathrm{in}\mathrm{the}\mathrm{expansion}\mathrm{of}{(1+{\mathrm{x}}^2-{\mathrm{x}}^3)}^8$$ Answered by EDWIN88 last updated on 13/Feb/21 $$\mathrm{by}\:\mathrm{multinomial}\:\mathrm{theorem}\:;\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{10}} \…

Question Number 1074 by Yugi last updated on 05/Jun/15 $$ProvebyinductionthefollowingresultwhereNisapositiveeveninteger.$$$$S_1^2+S_2^2=2^N$$$${where}\:\:\:\:{S}_{\mathrm{1}} =\underset{{r}=\mathrm{1}} {\overset{\frac{{N}}{\mathrm{2}}+\mathrm{1}} {\sum}}\left(−\mathrm{1}\right)^{{r}−\mathrm{1}} $$\left(\begin{array}{c}N\\ 2(r-1)\end{array}\right)$$\:\:\:\:{and}\:\:\:\:\:\:{S}_{\mathrm{2}} =\underset{{r}=\mathrm{1}} {\overset{{N}/\mathrm{2}} {\sum}}\left(−\mathrm{1}\right)^{{r}+\mathrm{1}}…

Question Number 131994 by liberty last updated on 10/Feb/21 Commented by liberty last updated on 10/Feb/21 $$\mathrm{old}\mathrm{unswered}$$ Answered by EDWIN88 last updated on…