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Category: Permutation and Combination

Question-172354

Question Number 172354 by Mikenice last updated on 25/Jun/22 Answered by mahdipoor last updated on 25/Jun/22 $${log}_{{a}} {b}={m}\:\:\:\:{log}_{{a}} {c}={n} \\ $$$$\Rightarrow\begin{cases}{{log}_{{n}^{\mathrm{2}} } \left(\mathrm{1}/{m}\right)=−\frac{\mathrm{1}}{\mathrm{2}}{log}_{{n}} {m}=\frac{−\mathrm{3}}{\mathrm{2}}}\\{\frac{{log}_{{a}} {b}}{{log}_{{a}}…

please-help-me-to-show-that-the-equation-X-n-aX-c-0-can-not-have-more-than-3-reals-solutions-

Question Number 106815 by pticantor last updated on 07/Aug/20 $$\:\:\:\boldsymbol{{please}}\:\boldsymbol{{help}}\:\boldsymbol{{me}}\:\boldsymbol{{to}}\:\boldsymbol{{show}} \\ $$$$\boldsymbol{{that}}\:\:\boldsymbol{{the}}\:\boldsymbol{{equation}}\: \\ $$$$\:\boldsymbol{{X}}^{\boldsymbol{{n}}} +\boldsymbol{{aX}}+\boldsymbol{{c}}=\mathrm{0}\:\boldsymbol{{can}}\:\boldsymbol{{not}}\:\boldsymbol{{have}} \\ $$$$\boldsymbol{{more}}\:\boldsymbol{{than}}\:\mathrm{3}\:\boldsymbol{{reals}}\:\boldsymbol{{solutions}} \\ $$$$ \\ $$ Answered by 1549442205PVT last…

bobhans-From-a-batch-containing-6-boys-and-4-girls-a-group-of-4-students-is-tobe-selected-How-many-group-formations-will-have-exactly-2-girls-

Question Number 106792 by bobhans last updated on 07/Aug/20 $$\:\:\:\:\:\:\succ\mathrm{bobhans}\prec \\ $$$$\mathrm{From}\:\mathrm{a}\:\mathrm{batch}\:\mathrm{containing}\:\mathrm{6}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{4}\:\mathrm{girls} \\ $$$$\mathrm{a}\:\mathrm{group}\:\mathrm{of}\:\mathrm{4}\:\mathrm{students}\:\mathrm{is}\:\mathrm{tobe}\:\mathrm{selected}\:. \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{group}\:\mathrm{formations}\:\mathrm{will}\:\mathrm{have} \\ $$$$\mathrm{exactly}\:\mathrm{2}\:\mathrm{girls}? \\ $$ Answered by bemath last updated…

what-is-probability-of-5-coming-up-at-least-one-if-a-die-is-rolled-3-times-

Question Number 106305 by bemath last updated on 04/Aug/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{5}\:\mathrm{coming}\:\mathrm{up}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{if}\:\mathrm{a}\:\mathrm{die}\: \\ $$$$\mathrm{is}\:\mathrm{rolled}\:\mathrm{3}\:\mathrm{times}\: \\ $$ Answered by Ar Brandon last updated on 04/Aug/20 $$\mathrm{P}\left(\mathrm{Atleast}\:\mathrm{one}\:\mathrm{5}\right)=\mathrm{1}−\mathrm{P}\left(\mathrm{No}\:\mathrm{5}\right) \\ $$$$\mathrm{P}\left(\mathrm{No}\:\mathrm{5}\right)=\left(\frac{\mathrm{5}}{\mathrm{6}}\right)^{\mathrm{3}}…

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Question Number 106292 by bemath last updated on 04/Aug/20 $$\mathrm{a}\:\mathrm{box}\:\mathrm{contains}\:\mathrm{4}\:\mathrm{blue},\:\mathrm{3}\:\mathrm{green}\:\mathrm{and}\:\mathrm{2}\:\mathrm{red}\:\mathrm{identicall}\:\mathrm{balls}.\: \\ $$$$\mathrm{if}\:\mathrm{two}\:\mathrm{balls}\:\mathrm{are}\:\mathrm{selected}\:\mathrm{at}\:\mathrm{random}\:\mathrm{without}\: \\ $$$$\mathrm{replacement}\:,\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability} \\ $$$$\mathrm{that}\:\mathrm{two}\:\mathrm{balls}\:\mathrm{be}\:\mathrm{of}\:\mathrm{the}\:\mathrm{same}\:\mathrm{colours}? \\ $$ Answered by bobhans last updated on 04/Aug/20…