Category: Permutation and Combination

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

Question Number 105853 by bobhans last updated on 01/Aug/20 $$Aboxcontains5balls,2ballswere$$$$drawnatrandom,bothofwhich$$$$turnedouttobewhite.whatisthe$$$$probabilitythatalltheballsinthebox$$$$arewhite?$$ Commented by bobhans last updated…

Question Number 40216 by scientist last updated on 17/Jul/18 Answered by math1967 last updated on 17/Jul/18 $$\overset{{n}} {\:}{c}_{{r}} +\overset{{n}} {\:}{c}_{{r}−\mathrm{1}} +\:^{{n}} {c}_{{r}−\mathrm{1}} +\overset{{n}} {\:}{c}_{{r}−\mathrm{2}} \…

Question Number 105551 by mr W last updated on 29/Jul/20 $$Inhowmanydifferentwayscan10$$$$studentsbedividedinto3groups?$$ Answered by adhigenz last updated on 29/Jul/20 $$\mathrm{It}\mathrm{is}\mathrm{the}\mathrm{same}\mathrm{thing}\mathrm{as}\mathrm{finding}\mathrm{how}$$$$\mathrm{many}\:\mathrm{possible}\:\mathrm{integer}\:\mathrm{solution}\:\mathrm{for}…

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