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Category: Permutation and Combination

Number-of-4-digited-numbers-with-distinct-digits-are-divisible-by-9-i-got-516-i-got-confusion-kidly-help-me-

Question Number 179358 by SLVR last updated on 28/Oct/22 $${Number}\:{of}\:\mathrm{4}\:{digited}\:\:{numbers}\: \\ $$$${with}\:{distinct}\:{digits}…{are}\:{divisible} \\ $$$${by}\:\mathrm{9}..{i}\:{got}\:\mathrm{516}…{i}\:{got}\:{confusion} \\ $$$${kidly}\:{help}\:{me} \\ $$ Commented by mr W last updated on…

you-have-2-identical-mathematics-books-2-identical-physics-books-2-identical-chemistry-books-2-identical-biology-books-and-2-geography-books-in-how-many-ways-can-you-compile-these-books-such-that-

Question Number 113710 by mr W last updated on 14/Sep/20 $${you}\:{have}\:\mathrm{2}\:{identical}\:{mathematics} \\ $$$${books},\:\mathrm{2}\:{identical}\:{physics}\:{books},\:\mathrm{2} \\ $$$${identical}\:{chemistry}\:{books},\:\mathrm{2}\:{identical} \\ $$$${biology}\:{books}\:{and}\:\mathrm{2}\:{geography}\:{books}. \\ $$$${in}\:{how}\:{many}\:{ways}\:{can}\:{you}\:{compile} \\ $$$${these}\:{books}\:{such}\:{that}\:{same}\:{books} \\ $$$${are}\:{not}\:{mutually}\:{adjacent}? \\ $$…

Find-the-greatest-coefficient-in-expansion-of-6-4x-3-

Question Number 178937 by Tawa11 last updated on 22/Oct/22 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{in}\:\mathrm{expansion}\:\mathrm{of}:\:\:\:\:\left(\mathrm{6}\:\:\:−\:\:\:\mathrm{4x}\right)^{−\:\:\mathrm{3}} \\ $$ Answered by mr W last updated on 23/Oct/22 $$\left(\mathrm{6}−\mathrm{4}{x}\right)^{−\mathrm{3}} \\ $$$$=\mathrm{6}^{−\mathrm{3}} \left(\mathrm{1}−\frac{\mathrm{2}{x}}{\mathrm{3}}\right)^{−\mathrm{3}} \\…

There-are-4-identical-mathematics-books-3-identical-physics-books-2-identical-chemistry-books-in-how-many-ways-can-you-compile-the-9-books-such-that-same-books-are-not-mutually-adjacent-

Question Number 113368 by mr W last updated on 12/Sep/20 $$\mathrm{There}\:\mathrm{are}\:\mathrm{4}\:\mathrm{identical}\:\mathrm{mathematics} \\ $$$$\mathrm{books},\:\mathrm{3}\:\mathrm{identical}\:\mathrm{physics}\:\mathrm{books},\:\mathrm{2} \\ $$$$\mathrm{identical}\:\mathrm{chemistry}\:\mathrm{books}. \\ $$$$\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\:\mathrm{can}\:\mathrm{you}\:\mathrm{compile} \\ $$$$\mathrm{the}\:\mathrm{9}\:\mathrm{books}\:\mathrm{such}\:\mathrm{that}\:\mathrm{same}\:\mathrm{books}\:\mathrm{are} \\ $$$$\mathrm{not}\:\mathrm{mutually}\:\mathrm{adjacent}. \\ $$ Answered by…

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 113355 by Aina Samuel Temidayo last updated on 12/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…

What-is-the-maximum-number-of-points-to-be-distributed-within-a-3-6-to-ensure-that-there-are-no-two-points-whose-distance-apart-is-less-than-2-

Question Number 113353 by Aina Samuel Temidayo last updated on 12/Sep/20 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{points}\:\mathrm{to}\:\mathrm{be}\:\mathrm{distributed}\:\mathrm{within} \\ $$$$\mathrm{a}\:\mathrm{3}×\mathrm{6}\:\mathrm{to}\:\mathrm{ensure}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{no}\:\mathrm{two} \\ $$$$\mathrm{points}\:\mathrm{whose}\:\mathrm{distance}\:\mathrm{apart}\:\mathrm{is}\:\mathrm{less} \\ $$$$\mathrm{than}\:\sqrt{\mathrm{2}}? \\ $$ Answered by mr…

A-square-is-divided-into-9-identical-smaller-squares-Six-identical-balls-are-to-be-placed-in-these-smaller-squares-such-that-each-of-the-three-rows-gets-at-least-one-ball-one-ball-in-one-square-only-

Question Number 47656 by Necxx last updated on 12/Nov/18 $${A}\:{square}\:{is}\:{divided}\:{into}\:\mathrm{9}\:{identical} \\ $$$${smaller}\:{squares}.{Six}\:{identical}\:{balls} \\ $$$${are}\:{to}\:{be}\:{placed}\:{in}\:{these}\:{smaller}\: \\ $$$${squares}\:{such}\:{that}\:{each}\:{of}\:{the}\:{three} \\ $$$${rows}\:{gets}\:{at}\:{least}\:{one}\:{ball}\left({one}\right. \\ $$$$\left.{ball}\:{in}\:{one}\:{square}\:{only}\right).{In}\:{how} \\ $$$${many}\:{different}\:{ways}\:{can}\:{this}\:{be} \\ $$$${done}? \\…