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Category: Permutation and Combination

A-rectangular-cardboard-is-8cm-long-and-6cm-wide-What-is-the-least-number-of-beads-you-can-arrange-on-the-board-such-that-there-are-at-least-two-of-the-beads-that-are-less-than-10-cm-apart-

Question Number 112531 by Aina Samuel Temidayo last updated on 08/Sep/20 $$\mathrm{A}\:\mathrm{rectangular}\:\mathrm{cardboard}\:\mathrm{is}\:\mathrm{8cm}\:\mathrm{long} \\ $$$$\mathrm{and}\:\mathrm{6cm}\:\mathrm{wide}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{least} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{beads}\:\mathrm{you}\:\mathrm{can}\:\mathrm{arrange}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{board}\:\mathrm{such}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{at}\:\mathrm{least} \\ $$$$\mathrm{two}\:\mathrm{of}\:\mathrm{the}\:\mathrm{beads}\:\mathrm{that}\:\mathrm{are}\:\mathrm{less}\:\mathrm{than} \\ $$$$\sqrt{\mathrm{10}}\mathrm{cm}\:\mathrm{apart}. \\ $$ Commented…

n-1-11-1-n-1-4n-2-4n-n-1-please-help-

Question Number 112195 by 675480065 last updated on 06/Sep/20 $$\underset{\mathrm{n}=\mathrm{1}\:} {\overset{\mathrm{11}} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}+\mathrm{1}} \left(\mathrm{4n}+\mathrm{2}\right)}{\mathrm{4n}\left(\mathrm{n}+\mathrm{1}\right)} \\ $$$$\mathrm{please}\:\mathrm{help} \\ $$ Answered by MJS_new last updated on 06/Sep/20 $$\mathrm{simply}\:\mathrm{calculate}\:\mathrm{it}!\:\mathrm{it}'\mathrm{s}\:\mathrm{only}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{11}…

Question-177597

Question Number 177597 by cortano1 last updated on 07/Oct/22 Answered by mr W last updated on 07/Oct/22 $$\boldsymbol{{method}}\:\mathrm{1}:\:\boldsymbol{{without}}\:\boldsymbol{{using}}\:\boldsymbol{{formula}} \\ $$$$\mathrm{1}×\mathrm{1}×{C}_{\mathrm{3}} ^{\mathrm{6}} ×\mathrm{2}^{\mathrm{3}} \\ $$$$+\left[\mathrm{1}×\left(−\mathrm{1}\right)+\mathrm{3}×\mathrm{1}\right]×{C}_{\mathrm{2}} ^{\mathrm{6}}…

Question-111937

Question Number 111937 by bemath last updated on 05/Sep/20 Answered by bobhans last updated on 05/Sep/20 $$\:\mathrm{let}\:\mathrm{the}\:\mathrm{first}\:\mathrm{five}\:\mathrm{question}\:\mathrm{is}\:\mathrm{number}\::\: \\ $$$$\mathrm{1};\:\mathrm{2};\:\mathrm{3};\:\mathrm{4};\:\mathrm{5}\: \\ $$$$\mathrm{case}\left(\mathrm{1}\right)\:\Rightarrow\:\mathrm{C}\:_{\mathrm{4}} ^{\mathrm{5}} \:×\:\mathrm{C}\:_{\mathrm{4}} ^{\mathrm{5}} \:=\:\mathrm{25}\:…

Question-111906

Question Number 111906 by mr W last updated on 05/Sep/20 Answered by PRITHWISH SEN 2 last updated on 22/Sep/20 $$\mathrm{Disarrangement}\:\mathrm{of}\:\mathrm{6}\:\mathrm{cards}\:!\mathrm{6}=\mathrm{265} \\ $$$$\mathrm{now}\:\mathrm{in}\:\mathrm{this}\:\mathrm{265}\:\mathrm{ways}\:\mathrm{card}\:\mathrm{no}.\:\mathrm{1}\:\mathrm{can}\:\mathrm{be}\:\mathrm{in}\: \\ $$$$\mathrm{envelope}\:\mathrm{no}.\:\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\:\mathrm{or}\:\mathrm{6}\:\mathrm{and}\:\mathrm{in}\:\mathrm{each}\:\mathrm{case}\:\mathrm{the} \\…

How-many-3-digited-numbers-which-are-divisible-by-1-3-2-4-3-5-4-6-5-7-6-8-7-9-with-repetetion-of-digits-is-NOT-allowed-one-problem-process-

Question Number 177309 by SLVR last updated on 03/Oct/22 $${How}\:{many}\:\mathrm{3}\:{digited}\:{numbers}\: \\ $$$$\left.{which}\:{are}\:{divisible}\:{by}\:\mathrm{1}\right)\mathrm{3} \\ $$$$\left.\mathrm{2}\left.\right)\left.\mathrm{4}\left.\:\left.\:\left.\:\:\mathrm{3}\right)\mathrm{5}\:\:\:\:\mathrm{4}\right)\mathrm{6}\:\:\:\mathrm{5}\right)\mathrm{7}\:\:\:\:\mathrm{6}\right)\mathrm{8}\:\:\mathrm{7}\right)\mathrm{9} \\ $$$${with}\:{repetetion}\:{of}\:{digits}\:{is} \\ $$$${NOT}\:{allowed}…{one}\:{problem}\:{process} \\ $$ Commented by SLVR last updated…

A-blind-man-is-to-place-5-letters-into-5-pigeon-holes-how-many-ways-can-4-of-the-letters-be-wrongly-placed-note-that-only-one-letter-must-be-in-a-pigeon-hole-

Question Number 111732 by Aina Samuel Temidayo last updated on 04/Sep/20 $$\mathrm{A}\:\mathrm{blind}\:\mathrm{man}\:\mathrm{is}\:\mathrm{to}\:\mathrm{place}\:\mathrm{5}\:\mathrm{letters}\:\mathrm{into}\:\mathrm{5} \\ $$$$\mathrm{pigeon}\:\mathrm{holes},\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{4}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{letters}\:\mathrm{be}\:\mathrm{wrongly}\:\mathrm{placed}? \\ $$$$\left(\mathrm{note}\:\mathrm{that}\:\mathrm{only}\:\mathrm{one}\:\mathrm{letter}\:\mathrm{must}\:\mathrm{be}\:\mathrm{in}\:\mathrm{a}\right. \\ $$$$\left.\mathrm{pigeon}\:\mathrm{hole}\right) \\ $$ Answered by mr…

Question-177008

Question Number 177008 by Ar Brandon last updated on 29/Sep/22 Answered by Rasheed.Sindhi last updated on 29/Sep/22 $${Let}\:{t}\:{is}\:{total}\:{of}\:{card}\:{numbers}\:{chose}\:{by}\:{players}. \\ $$$${Efe}'{s}\:{card}\:{number}=\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\mathrm{6}\leqslant{t}\leqslant\mathrm{20} \\ $$$${If}\:{t}\in\mathbb{P}\:{then}\:{possible}\:{values}\:{for}\:{t}: \\…