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Category: Permutation and Combination

An-unfair-coin-with-the-probability-of-getting-head-in-one-toss-1-5-If-coin-tosses-n-times-the-probability-of-getting-2-heads-is-equal-to-the-probability-of-getting-3-heads-Find-n-

Question Number 43659 by Joel578 last updated on 13/Sep/18 $$\mathrm{An}\:\mathrm{unfair}\:\mathrm{coin}\:\mathrm{with}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{getting} \\ $$$$\mathrm{head}\:\mathrm{in}\:\mathrm{one}\:\mathrm{toss}\:=\:\frac{\mathrm{1}}{\mathrm{5}}. \\ $$$$\mathrm{If}\:\mathrm{coin}\:\mathrm{tosses}\:{n}\:\mathrm{times},\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of} \\ $$$$\mathrm{getting}\:\mathrm{2}\:\mathrm{heads}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\: \\ $$$$\mathrm{getting}\:\mathrm{3}\:\mathrm{heads}.\:\mathrm{Find}\:{n} \\ $$ Commented by math1967 last updated…

how-many-odd-numbers-greater-than-60000-can-be-made-from-the-digits-5-6-7-8-9-0-if-no-number-contains-any-digit-more-than-once-

Question Number 43343 by pieroo last updated on 10/Sep/18 $$\mathrm{how}\:\mathrm{many}\:\mathrm{odd}\:\mathrm{numbers}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{60000}\:\mathrm{can}\:\mathrm{be}\:\mathrm{made} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{5},\mathrm{6},\mathrm{7},\mathrm{8},\mathrm{9},\mathrm{0}\:\mathrm{if}\:\mathrm{no}\:\mathrm{number}\:\mathrm{contains} \\ $$$$\mathrm{any}\:\mathrm{digit}\:\mathrm{more}\:\mathrm{than}\:\mathrm{once}? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 10/Sep/18 $$\underset{\mathrm{5}} {−}\:\underset{\mathrm{4}}…

BeMath-1-find-1-2-2-0-pi-2-x-sin-x-1-cos-x-2-dx-

Question Number 108450 by bemath last updated on 17/Aug/20 $$\:\:\frac{\mathcal{B}{e}\mathcal{M}{ath}}{\subset\supset} \\ $$$$\left(\mathrm{1}\right){find}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\right)! \\ $$$$\left(\mathrm{2}\right)\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\frac{{x}\:\mathrm{sin}\:{x}}{\left(\mathrm{1}+\mathrm{cos}\:{x}\right)^{\mathrm{2}} }\:{dx} \\ $$ Commented by Smail last updated on…

0-y-a-1-1-y-b-dy-u-1-1-y-0-1-1-u-a-1-u-a-1-u-b-du-u-2-0-1-u-b-a-1-1-u-a-1-du-

Question Number 173975 by savitar last updated on 22/Jul/22 $$ \\ $$$$\: \\ $$$$ \\ $$$$\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{{y}^{{a}−\mathrm{1}} }{\left(\mathrm{1}+{y}\right)^{{b}} }\:{dy}\:\overset{{u}=\frac{\mathrm{1}}{\mathrm{1}+{y}}} {=}\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left(\mathrm{1}−{u}\right)^{{a}−\mathrm{1}} }{{u}^{{a}−\mathrm{1}} }\:{u}^{{b}}…

In-the-sequence-of-numbers-1-2-11-22-111-222-the-sum-of-the-digits-in-999th-terms-is-

Question Number 42494 by Tawa1 last updated on 26/Aug/18 $$\mathrm{In}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{of}\:\mathrm{numbers}\:\:\mathrm{1},\:\mathrm{2},\:\mathrm{11},\:\mathrm{22},\:\mathrm{111},\:\mathrm{222},\:…\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits} \\ $$$$\mathrm{in}\:\mathrm{999th}\:\mathrm{terms}\:\mathrm{is}\:?? \\ $$ Commented by Tinku Tara last updated on 22/Apr/21 $$\mathrm{1st}\:\mathrm{term}\:\mathrm{1} \\ $$$$\mathrm{3rd}\:\mathrm{term}\:\mathrm{11}…