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Category: Permutation and Combination

given-f-x-cx-x-20-and-A-2-5-find-the-nearst-point-to-A-on-the-graph-

Question Number 192256 by Red1ight last updated on 13/May/23 $$\mathrm{given}\:{f}\left({x}\right)={cx}\left({x}−\mathrm{20}\right)\:\mathrm{and}\:{A}=\left(\mathrm{2},\mathrm{5}\right) \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{nearst}\:\mathrm{point}\:\mathrm{to}\:{A}\:\mathrm{on}\:\mathrm{the}\:\mathrm{graph} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

How-many-four-digit-numbers-between-2000-and-4000-can-be-formed-from-the-numbers-0-1-2-3-4-and-5-if-repitition-is-allowed-

Question Number 125548 by Don08q last updated on 12/Dec/20 $$\mathrm{How}\:\mathrm{many}\:\mathrm{four}−\mathrm{digit}\:\mathrm{numbers}\: \\ $$$$\mathrm{between}\:\mathrm{2000}\:\mathrm{and}\:\mathrm{4000}\:\mathrm{can}\:\mathrm{be}\:\mathrm{formed} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{numbers}\:\mathrm{0},\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4}\:\mathrm{and}\:\mathrm{5}\: \\ $$$$\mathrm{if}\:\mathrm{repitition}\:\mathrm{is}\:\mathrm{allowed}? \\ $$ Commented by liberty last updated on 13/Dec/20…

In-a-room-containing-N-people-N-gt-3-at-least-one-person-has-not-shaken-hands-with-everyone-else-in-the-room-What-is-the-maximum-number-of-people-in-the-room-that-could-have-shaken-hands-with-ev

Question Number 125460 by john_santu last updated on 11/Dec/20 $$\:{In}\:{a}\:{room}\:{containing}\:{N}\:{people} \\ $$$${N}>\mathrm{3},\:{at}\:{least}\:{one}\:{person}\:{has}\:{not} \\ $$$${shaken}\:{hands}\:{with}\:{everyone} \\ $$$${else}\:{in}\:{the}\:{room}.\:{What}\:{is}\:{the}\: \\ $$$${maximum}\:{number}\:{of}\:{people}\: \\ $$$${in}\:{the}\:{room}\:{that}\:{could}\:{have}\: \\ $$$${shaken}\:{hands}\:{with}\:{everyone}\: \\ $$$${else}?\: \\…

There-are-12-students-in-a-party-Five-of-them-are-girls-In-how-many-ways-can-these-12-students-be-arranged-in-a-row-if-i-there-are-no-restrictions-ii-the-5-girls-must-be-together-forming-a-b

Question Number 125208 by liberty last updated on 09/Dec/20 $${There}\:{are}\:\mathrm{12}\:{students}\:{in}\:{a}\:{party}.\:{Five}\:{of} \\ $$$${them}\:{are}\:{girls}.\:{In}\:{how}\:{many}\:{ways}\:{can}\: \\ $$$${these}\:\mathrm{12}\:{students}\:{be}\:{arranged}\:{in}\:{a}\:{row}\:{if}\: \\ $$$$\left({i}\right)\:{there}\:{are}\:{no}\:{restrictions}? \\ $$$$\left({ii}\right)\:{the}\:\mathrm{5}\:{girls}\:{must}\:{be}\:{together}\:\left({forming}\:{a}\:{block}\right)? \\ $$$$\left({iii}\right)\:{no}\:\mathrm{2}\:{girls}\:{are}\:{adjacent}\: \\ $$$$\left({iv}\right)\:{between}\:{two}\:{particular}\:{boys}\:{A}\:{and}\:{B}\: \\ $$$$\:,\:{there}\:{no}\:{boys}\:{but}\:{exactly}\:\mathrm{3}\:{girls}? \\…

Find-the-number-of-ways-to-choose-a-pair-a-b-of-distinct-numbers-from-the-set-1-2-3-50-such-that-i-a-b-5-ii-a-b-5-

Question Number 125207 by liberty last updated on 09/Dec/20 $${Find}\:{the}\:{number}\:{of}\:{ways}\:{to}\:{choose}\:{a}\:{pair} \\ $$$$\left\{{a},{b}\right\}\:{of}\:{distinct}\:{numbers}\:{from}\:{the}\:{set}\: \\ $$$$\left\{\mathrm{1},\mathrm{2},\mathrm{3},…,\mathrm{50}\right\}\:{such}\:{that}\: \\ $$$$\left({i}\right)\:\mid{a}−{b}\mid\:=\:\mathrm{5} \\ $$$$\left({ii}\right)\:\mid{a}−{b}\mid\:\leqslant\:\mathrm{5}\: \\ $$ Answered by talminator2856791 last updated…