Menu Close

Category: Permutation and Combination

in-how-many-ways-can-the-number-n-be-written-as-a-sum-of-three-positive-integers-if-representations-differing-in-the-order-of-the-terms-are-considered-to-be-different-

Tinku Tara 0 Comments

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…

Read more →

Let-A-1-2-3-n-if-a-i-is-the-minimum-element-of-the-set-A-where-A-denotes-the-subset-of-A-containing-exactly-three-elements-and-X-denotes-the-set-of-A-i-s-then-evaluate-A-i-X-

Tinku Tara 0 Comments

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…

Read more →

Determine-the-number-of-ordered-pairs-of-positive-integers-a-b-such-that-the-least-common-multiple-of-a-and-b-is-2-3-5-7-11-13-

Tinku Tara 0 Comments

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…

Read more →

In-how-many-ways-we-can-choose-3-squares-on-a-chess-board-such-that-one-of-the-squares-has-its-two-sides-common-to-other-two-squares-

Tinku Tara 0 Comments

Question Number 22043 by Tinkutara last updated on 10/Oct/17 $$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{we}\:\mathrm{can}\:\mathrm{choose}\:\mathrm{3} \\ $$$$\mathrm{squares}\:\mathrm{on}\:\mathrm{a}\:\mathrm{chess}\:\mathrm{board}\:\mathrm{such}\:\mathrm{that}\:\mathrm{one} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{squares}\:\mathrm{has}\:\mathrm{its}\:\mathrm{two}\:\mathrm{sides}\:\mathrm{common} \\ $$$$\mathrm{to}\:\mathrm{other}\:\mathrm{two}\:\mathrm{squares}? \\ $$ Answered by Rasheed.Sindhi last updated on 10/Oct/17…

Read more →