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Category: Permutation and Combination

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}}…

a-box-contains-4-blue-3-green-and-2-red-identicall-balls-if-two-balls-are-selected-at-random-without-replacement-what-is-the-probability-that-two-balls-be-of-the-same-colours-

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…

if-three-numbers-are-drawn-at-random-successively-without-replacement-from-a-set-S-1-2-10-then-probability-that-the-minimum-of-the-choosen-number-is-3-or-their-maximum-is-7-Answer-11

Question Number 40550 by vajpaithegrate@gmail.com last updated on 24/Jul/18 $$\mathrm{if}\:\mathrm{three}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{drawn}\:\mathrm{at}\:\mathrm{random} \\ $$$$\mathrm{successively}\:\mathrm{without}\:\mathrm{replacement}\:\mathrm{from} \\ $$$$\mathrm{a}\:\mathrm{set}\:\mathrm{S}=\left\{\mathrm{1},\mathrm{2},……\mathrm{10}\right\}\mathrm{then}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{minimum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{choosen}\:\mathrm{number}\:\mathrm{is} \\ $$$$\mathrm{3}\:\mathrm{or}\:\mathrm{their}\:\mathrm{maximum}\:\mathrm{is}\:\mathrm{7}\:\:\:\:\:\:\:\: \\ $$$$\:\mathrm{Answer}=\frac{\mathrm{11}}{\mathrm{40}} \\ $$ Answered by tanmay.chaudhury50@gmail.com…

Given-2log-5-x-2-log-5-y-1-2-0-log-5-x-2-2x-2-0-find-the-value-of-y-

Question Number 105994 by bemath last updated on 02/Aug/20 $$\mathbb{G}{iven}\:\begin{cases}{\mathrm{2log}\:_{\mathrm{5}} \left({x}+\mathrm{2}\right)−\mathrm{log}\:_{\mathrm{5}} \left({y}\right)+\frac{\mathrm{1}}{\mathrm{2}}=\mathrm{0}}\\{\mathrm{log}\:_{\mathrm{5}} \left({x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{2}\right)=\mathrm{0}\:}\end{cases} \\ $$$${find}\:{the}\:{value}\:{of}\:{y}\: \\ $$ Commented by PRITHWISH SEN 2 last updated…

A-box-contains-5-balls-2-balls-were-drawn-at-random-both-of-which-turned-out-tobe-white-what-is-the-probability-that-all-the-balls-in-the-box-are-white-

Question Number 105853 by bobhans last updated on 01/Aug/20 $${A}\:{box}\:{contains}\:\mathrm{5}\:{balls},\:\mathrm{2}\:{balls}\:{were} \\ $$$${drawn}\:{at}\:{random},\:{both}\:{of}\:{which} \\ $$$${turned}\:{out}\:{tobe}\:{white}.\:{what}\:{is}\:{the} \\ $$$${probability}\:{that}\:{all}\:{the}\:{balls}\:{in}\:{the}\:{box} \\ $$$${are}\:{white}\:? \\ $$ Commented by bobhans last updated…