Question Number 87732 by mathocean1 last updated on 05/Apr/20 $$\mathrm{Solve}\:\mathrm{it}\:\mathrm{in}\:\mathbb{N} \\ $$$$\mathrm{C}_{\mathrm{n}} ^{\mathrm{3}} −\mathrm{C}_{\mathrm{n}} ^{\mathrm{2}} =\mathrm{5}+\frac{\mathrm{n}^{\mathrm{3}} −\mathrm{6n}^{\mathrm{2}} }{\mathrm{6}} \\ $$ Commented by Tony Lin last…
Question Number 153220 by talminator2856791 last updated on 05/Sep/21 $$\: \\ $$$$\:\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{the}\:\mathrm{number}\:\: \\ $$$$\:{n}\:\mathrm{be}\:\mathrm{written}\:\mathrm{as}\:\mathrm{a}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{three}\:\mathrm{positive}\:\: \\ $$$$\:\mathrm{integers}\:\mathrm{if}\:\mathrm{representations}\:\mathrm{differing}\:\: \\ $$$$\:\mathrm{in}\:\mathrm{the}\:\mathrm{order}\:\mathrm{of}\:\mathrm{the}\:\mathrm{terms}\:\mathrm{are}\:\mathrm{considered}\:\: \\ $$$$\:\mathrm{to}\:\mathrm{be}\:\mathrm{different}?\:\: \\ $$$$\: \\ $$ Answered…
Question Number 153216 by talminator2856791 last updated on 05/Sep/21 $$ \\ $$ Commented by talminator2856791 last updated on 05/Sep/21 $$\:\mathrm{appears}\:\mathrm{to}\:\mathrm{be}\:\mathrm{a}\:\mathrm{bug}. \\ $$$$\:\mathrm{image}\:\mathrm{not}\:\mathrm{load}. \\ $$ Terms…
Question Number 22128 by devika last updated on 11/Oct/17 Commented by Samuel KT last updated on 11/Oct/17 $$\mathrm{what}'\mathrm{s}\:\mathrm{the}\:\mathrm{question}?? \\ $$ Commented by $@ty@m last updated…
Question Number 153181 by DELETED last updated on 05/Sep/21 Commented by mr W last updated on 05/Sep/21 $${dear}\:{sir}: \\ $$$${if}\:{you}\:{just}\:{do}\:{your}\:{own}\:{exercises},\:{i}.{e}. \\ $$$${when}\:{you}\:{solve}\:{your}\:{questions}\:{by} \\ $$$${yourself},\:{you}\:{don}'{t}\:{need}\:{to}\:{use}\:{the} \\…
Question Number 153182 by DELETED last updated on 05/Sep/21 Commented by mr W last updated on 05/Sep/21 $${dear}\:{sir}: \\ $$$${if}\:{you}\:{just}\:{do}\:{your}\:{own}\:{exercises},\:{i}.{e}. \\ $$$${when}\:{you}\:{solve}\:{your}\:{questions}\:{by} \\ $$$${yourself},\:{you}\:{don}'{t}\:{need}\:{to}\:{use}\:{the} \\…
Question Number 153173 by DELETED last updated on 05/Sep/21 Commented by mr W last updated on 05/Sep/21 $${dear}\:{sir}: \\ $$$${if}\:{you}\:{just}\:{do}\:{your}\:{own}\:{exercises},\:{i}.{e}. \\ $$$${when}\:{you}\:{solve}\:{your}\:{questions}\:{by} \\ $$$${yourself},\:{you}\:{don}'{t}\:{need}\:{to}\:{use}\:{the} \\…
Question Number 153174 by DELETED last updated on 05/Sep/21 Commented by mr W last updated on 05/Sep/21 $${dear}\:{sir}: \\ $$$${if}\:{you}\:{just}\:{do}\:{your}\:{own}\:{exercises},\:{i}.{e}. \\ $$$${when}\:{you}\:{solve}\:{your}\:{questions}\:{by} \\ $$$${yourself},\:{you}\:{don}'{t}\:{need}\:{to}\:{use}\:{the} \\…
Question Number 22044 by Tinkutara last updated on 10/Oct/17 $$\mathrm{Let}\:{A}\:=\:\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:…..,\:{n}\right\},\:\mathrm{if}\:{a}_{{i}} \:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{minimum}\:\mathrm{element}\:\mathrm{of}\:\mathrm{the}\:\mathrm{set}\:{A};\:\left(\mathrm{where}\right. \\ $$$${A};\:\mathrm{denotes}\:\mathrm{the}\:\mathrm{subset}\:\mathrm{of}\:{A}\:\mathrm{containing} \\ $$$$\left.\mathrm{exactly}\:\mathrm{three}\:\mathrm{elements}\right)\:\mathrm{and}\:{X}\:\mathrm{denotes} \\ $$$$\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:{A}_{{i}} '\mathrm{s},\:\mathrm{then}\:\mathrm{evaluate}\:\underset{{A}_{{i}} \in{X}} {\sum}{a}. \\ $$ Answered…
Question Number 22042 by Tinkutara last updated on 10/Oct/17 $$\mathrm{Determine}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ordered} \\ $$$$\mathrm{pairs}\:\mathrm{of}\:\mathrm{positive}\:\mathrm{integers}\:\left({a},\:{b}\right)\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{least}\:\mathrm{common}\:\mathrm{multiple}\:\mathrm{of}\:{a} \\ $$$$\mathrm{and}\:{b}\:\mathrm{is}\:\mathrm{2}^{\mathrm{3}} \centerdot\mathrm{5}^{\mathrm{7}} \centerdot\mathrm{11}^{\mathrm{13}} . \\ $$ Answered by Rasheed.Sindhi last…