Category: Permutation and Combination

Question Number 171011 by mr W last updated on 06/Jun/22 $$\mathrm{How}\mathrm{many}5-\mathrm{digit}\mathrm{numbers}\mathrm{from}\mathrm{the}$$$$\mathrm{digits}\{0,1,\dots ..,9\}\mathrm{have}?$$$$\left(\mathrm{i}\right)\mathrm{Strictly}\mathrm{increasing}\mathrm{digits}$$$$\left(\mathrm{ii}\right)\mathrm{Strictly}\mathrm{increasing}\mathrm{or}\mathrm{decreasing}$$$$\mathrm{digits}$$$$\left(\mathrm{iii}\right)\mathrm{Increasing}\mathrm{digits}$$$$\left(\mathrm{iv}\right)\mathrm{Increasing}\mathrm{or}\mathrm{decreasing}\mathrm{digits}$$…

Question Number 105265 by bemath last updated on 27/Jul/20 Answered by Cinezoidy1 last updated on 27/Jul/20 $$P(F_5\cup V)=P\left(F_5\right)+P\left(V\right)-P(F_5\cap V)$$$$P(F_5\cap V)=\frac{5letters}{26}+\frac{5vowels}{26}-\frac{2\left(aande\right)}{26}$$$${P}\left({F}_{\mathrm{5}}…

Question Number 104370 by bemath last updated on 21/Jul/20 Answered by john santu last updated on 21/Jul/20 $$\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◻"\; src="https://s.w.org/images/core/emoji/15.1.0/svg/25fb.svg">}△\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◻"\; src="https://s.w.org/images/core/emoji/15.1.0/svg/25fb.svg">}△$$$$\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◻"\; src="https://s.w.org/images/core/emoji/15.1.0/svg/25fb.svg">}=letter$$$$△=number$$$${password}\:=\:\mathrm{4}×\mathrm{4}×\mathrm{1}×\mathrm{6}\:=\:\mathrm{96}\:. \…

Question Number 104134 by bemath last updated on 19/Jul/20 $$whatisthecoefficient{x}^{15}$$$$intheexpansionof{x}^6{(1-x)}^{11}$$ Answered by bobhans last updated on 19/Jul/20 $$''\boldsymbol{{x}}^{\mathrm{6}} \left(\mathrm{1}−\boldsymbol{{x}}\right)^{\mathrm{11}} \:=\:\boldsymbol{{x}}^{\mathrm{6}}…

Question Number 103826 by bobhans last updated on 17/Jul/20 $$Intheexpansionof{(1+x)}^{20}ifthe$$$$coefficientof{x}^{r}istwicethecoefficient$$$$of{x}^{r-1},whatthevalueofthe$$$$coefficient?$$ Answered by bramlex last…