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Category: Permutation and Combination

How-many-6-digit-numbers-exist-whose-digits-have-exactly-the-sum-13-for-example-120505-is-such-a-number-

Question Number 102816 by mr W last updated on 11/Jul/20 $${How}\:{many}\:\mathrm{6}\:{digit}\:{numbers}\:{exist} \\ $$$${whose}\:{digits}\:{have}\:{exactly}\:{the}\:{sum}\:\mathrm{13}? \\ $$$$ \\ $$$${for}\:{example}\:\mathrm{120505}\:{is}\:{such}\:{a}\:{number}. \\ $$ Commented by Rasheed.Sindhi last updated on…

There-are-14-boys-and-10-girls-in-a-classroom-The-teacher-wants-to-form-a-team-of-5-students-The-team-must-have-a-least-two-boys-and-two-girls-Find-the-number-of-ways-the-team-can-be-chosen-

Question Number 102800 by bramlex last updated on 11/Jul/20 $$\mathrm{There}\:\mathrm{are}\:\mathrm{14}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{10}\:\mathrm{girls}\:\mathrm{in} \\ $$$$\mathrm{a}\:\mathrm{classroom}.\:\mathrm{The}\:\mathrm{teacher}\:\mathrm{wants} \\ $$$$\mathrm{to}\:\mathrm{form}\:\mathrm{a}\:\mathrm{team}\:\mathrm{of}\:\mathrm{5}\:\mathrm{students}\:. \\ $$$$\mathrm{The}\:\mathrm{team}\:\mathrm{must}\:\mathrm{have}\:\mathrm{a}\:\mathrm{least}\:\mathrm{two} \\ $$$$\mathrm{boys}\:\mathrm{and}\:\mathrm{two}\:\mathrm{girls}\:.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{the}\:\mathrm{team}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{chosen}.\: \\ $$ Answered…

3-men-and-4-women-are-to-sit-on-a-table-Calculate-the-number-of-possible-sitting-arrangements-if-a-they-sit-in-a-row-such-that-the-men-must-not-sit-next-to-each-other-b-they-

Question Number 167979 by nadovic last updated on 31/Mar/22 $$\mathrm{3}\:\mathrm{men}\:\mathrm{and}\:\mathrm{4}\:\mathrm{women}\:\mathrm{are}\:\mathrm{to}\:\mathrm{sit}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{table}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{possible}\:\mathrm{sitting}\:\mathrm{arrangements}\:\mathrm{if} \\ $$$$\:\left({a}\right)\:\mathrm{they}\:\mathrm{sit}\:\mathrm{in}\:\mathrm{a}\:\mathrm{row}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{men}\:\mathrm{must}\:\mathrm{not}\:\mathrm{sit}\:\mathrm{next}\:\mathrm{to}\:\mathrm{each} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{other}. \\ $$$$\:\left({b}\right)\:\mathrm{they}\:\mathrm{sit}\:\mathrm{in}\:\mathrm{circular}\:\mathrm{pattern}\:\mathrm{and} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{the}\:\mathrm{clockwise}\:\mathrm{and}\:\mathrm{anticlockwise} \\…

Consider-triangle-ABC-If-206-lines-are-drawn-from-A-to-BC-how-many-triangles-are-formed-

Question Number 36398 by NECx last updated on 01/Jun/18 $${Consider}\:{triangle}\:{ABC}.{If}\:\mathrm{206} \\ $$$${lines}\:{are}\:{drawn}\:{from}\:{A}\:{to}\:{BC}\:{how} \\ $$$${many}\:{triangles}\:{are}\:{formed}? \\ $$ Commented by Rasheed.Sindhi last updated on 02/Jun/18 $$\mathrm{207}+\mathrm{206}+…+\mathrm{1}=\frac{\mathrm{207}×\mathrm{208}}{\mathrm{2}}=\mathrm{21528} \\…

There-are-10-identical-mathematics-books-7-identical-physics-books-and-5-identical-chemistry-books-Find-the-number-of-ways-to-compile-the-books-under-the-condition-that-same-books-are-not-mutually-

Question Number 101732 by mr W last updated on 04/Jul/20 $$\mathrm{There}\:\mathrm{are}\:\mathrm{10}\:\mathrm{identical}\:\mathrm{mathematics} \\ $$$$\mathrm{books},\:\mathrm{7}\:\mathrm{identical}\:\mathrm{physics}\:\mathrm{books} \\ $$$$\mathrm{and}\:\mathrm{5}\:\mathrm{identical}\:\mathrm{chemistry}\:\mathrm{books}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{to}\:\mathrm{compile}\: \\ $$$$\mathrm{the}\:\mathrm{books}\:\mathrm{under}\:\mathrm{the}\:\mathrm{condition}\:\mathrm{that} \\ $$$$\mathrm{same}\:\mathrm{books}\:\mathrm{are}\:\mathrm{not}\:\mathrm{mutually}\:\mathrm{adjacent}. \\ $$ Commented by…