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Category: Permutation and Combination

an-integer-n-between-1-and-98-inclusive-is-to-be-chosen-at-random-what-is-the-probability-that-n-n-1-will-be-divisible-by-3-

Question Number 103606 by bemath last updated on 16/Jul/20 $${an}\:{integer}\:{n}\:{between}\:\mathrm{1}\:{and}\:\mathrm{98}\:, \\ $$$${inclusive}\:{is}\:{to}\:{be}\:{chosen}\:{at} \\ $$$${random}.\:{what}\:{is}\:{the}\:{probability} \\ $$$${that}\:{n}\left({n}+\mathrm{1}\right)\:{will}\:{be}\:{divisible}\:{by}\:\mathrm{3} \\ $$ Commented by bemath last updated on 16/Jul/20…

coefficient-of-x-5-in-expansion-1-x-2-5-1-x-4-equal-to-a-40-b-45-c-50-d-55-e-60-

Question Number 103513 by bemath last updated on 15/Jul/20 $${coefficient}\:{of}\:{x}^{\mathrm{5}} \:{in}\:{expansion} \\ $$$$\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{5}} \left(\mathrm{1}+{x}\right)^{\mathrm{4}} \:{equal}\:{to}\: \\ $$$$\left({a}\right)\:\mathrm{40}\:\:\:\:\:\:\left({b}\right)\:\mathrm{45}\:\:\:\:\:\left({c}\right)\:\mathrm{50}\:\:\:\:\left({d}\right)\:\mathrm{55} \\ $$$$\left({e}\right)\:\mathrm{60} \\ $$ Answered by OlafThorendsen…

100-students-are-standing-in-a-row-4-students-should-be-selected-in-the-way-that-no-two-of-them-are-next-to-each-other-how-many-ways-do-you-have-to-do-this-

Question Number 103406 by mr W last updated on 16/Jul/20 $$\mathrm{100}\:{students}\:{are}\:{standing}\:{in}\:{a}\:{row}. \\ $$$$\mathrm{4}\:{students}\:{should}\:{be}\:{selected}\:{in}\:{the} \\ $$$${way}\:{that}\:{no}\:{two}\:{of}\:{them}\:{are}\:{next}\:{to} \\ $$$${each}\:{other}.\:{how}\:{many}\:{ways}\:{do}\:{you} \\ $$$${have}\:{to}\:{do}\:{this}? \\ $$ Commented by bobhans last…

There-are-21-students-will-be-trained-with-6-trainers-available-Every-students-is-trained-by-1-coach-and-every-coach-trains-students-with-different-amounts-many-ways-of-grouping-students-who-will-be

Question Number 103357 by bobhans last updated on 14/Jul/20 $${There}\:{are}\:\mathrm{21}\:{students}\:{will}\:{be}\:{trained} \\ $$$${with}\:\mathrm{6}\:{trainers}\:{available}.\:{Every}\:{students} \\ $$$${is}\:{trained}\:{by}\:\mathrm{1}\:{coach}\:{and}\:{every}\:{coach} \\ $$$${trains}\:{students}\:{with}\:{different}\:{amounts}. \\ $$$${many}\:{ways}\:{of}\:{grouping}\:{students}\:{who} \\ $$$${will}\:{be}\:{trained}\:{are}\:…. \\ $$$$\left({a}\right)\:\frac{\mathrm{21}!}{\mathrm{6}!}\:\:\:\:\left({b}\right)\:\mathrm{6}!.\mathrm{21}!\:\:\:\:\:\left({c}\right)\:\frac{\mathrm{21}!}{\mathrm{2}!.\mathrm{3}!.\mathrm{4}!.\mathrm{5}!\:\:}\:\: \\ $$$$\left({d}\right)\:\mathrm{6}×\mathrm{21}!\:\:\:\:\left({e}\right)\:\frac{\mathrm{21}!}{\mathrm{15}!}×\mathrm{6}! \\…

many-positive-five-digit-integers-with-the-first-number-1-and-there-are-three-equal-numbers-a-810-b-720-c-120-d-60-e-20-

Question Number 103300 by bramlex last updated on 14/Jul/20 $$\mathrm{many}\:\mathrm{positive}\:\mathrm{five}−\mathrm{digit} \\ $$$$\mathrm{integers}\:\mathrm{with}\:\mathrm{the}\:\mathrm{first}\:\mathrm{number}\:\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{there}\:\mathrm{are}\:\mathrm{three}\:\mathrm{equal} \\ $$$$\mathrm{numbers}\:? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{810}\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{720}\:\:\:\:\left(\mathrm{c}\right)\mathrm{120} \\ $$$$\left(\mathrm{d}\right)\:\mathrm{60}\:\:\:\:\:\left(\mathrm{e}\right)\:\mathrm{20} \\ $$ Answered by bemath…

from-letters-in-MATEMATIKA-words-formed-by-using-all-the-letters-How-many-words-that-can-be-formed-with-the-five-consonant-are-always-side-by-side-

Question Number 103294 by bramlex last updated on 14/Jul/20 $$\mathrm{from}\:\mathrm{letters}\:\mathrm{in} \\ $$$$'\mathrm{MATEMATIKA}'\:\mathrm{words} \\ $$$$\mathrm{formed}\:\mathrm{by}\:\mathrm{using}\:\mathrm{all}\:\mathrm{the}\:\mathrm{letters}\:. \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{words}\:\mathrm{that}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{formed}\:\mathrm{with}\:\mathrm{the}\:\mathrm{five}\:\mathrm{consonant} \\ $$$$\mathrm{are}\:\mathrm{always}\:\mathrm{side}\:\mathrm{by}\:\mathrm{side}\: \\ $$ Answered by bemath…

A-particle-of-mass-5kg-moves-in-a-straight-line-its-displacement-x-metres-after-t-seconds-is-given-by-x-t-3-4t-2-4t-Find-the-magnitude-of-the-impulses-exerted-on-the-particle-when-t-2-

Question Number 37648 by Rio Mike last updated on 16/Jun/18 $$\mathrm{A}\:\mathrm{particle},\:\mathrm{of}\:\mathrm{mass}\:\mathrm{5kg},\mathrm{moves}\:\mathrm{in} \\ $$$$\mathrm{a}\:\mathrm{straight}\:\mathrm{line}\:\mathrm{its}\:\mathrm{displacement},\mathrm{x} \\ $$$$\mathrm{metres}\:\mathrm{after}\:\mathrm{t}\:\mathrm{seconds}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$$${x}\:=\:{t}^{\mathrm{3}} −\:\mathrm{4}{t}^{\mathrm{2}} +\mathrm{4}{t}.\:{F}\mathrm{ind}\:\:\mathrm{the}\:\mathrm{magnitude} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{impulses}\:\mathrm{exerted}\:\mathrm{on}\:\mathrm{the}\:\mathrm{particle} \\ $$$$\mathrm{when}\:\mathrm{t}=\mathrm{2}. \\ $$…