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Category: Permutation and Combination

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-

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…

On-the-modified-chess-board-10-10-Amit-and-Suresh-two-persons-which-start-moving-towards-each-other-Each-person-moving-with-same-constant-speed-Amit-can-move-only-to-the-right-and-upwards-along-t

Question Number 22041 by Tinkutara last updated on 10/Oct/17 $$\mathrm{On}\:\mathrm{the}\:\mathrm{modified}\:\mathrm{chess}\:\mathrm{board}\:\mathrm{10}\:×\:\mathrm{10}, \\ $$$$\mathrm{Amit}\:\mathrm{and}\:\mathrm{Suresh}\:\mathrm{two}\:\mathrm{persons}\:\mathrm{which} \\ $$$$\mathrm{start}\:\mathrm{moving}\:\mathrm{towards}\:\mathrm{each}\:\mathrm{other}.\:\mathrm{Each} \\ $$$$\mathrm{person}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{same}\:\mathrm{constant} \\ $$$$\mathrm{speed}.\:\mathrm{Amit}\:\mathrm{can}\:\mathrm{move}\:\mathrm{only}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{right}\:\mathrm{and}\:\mathrm{upwards}\:\mathrm{along}\:\mathrm{the}\:\mathrm{lines} \\ $$$$\mathrm{while}\:\mathrm{Suresh}\:\mathrm{can}\:\mathrm{move}\:\mathrm{only}\:\mathrm{to}\:\mathrm{the}\:\mathrm{left} \\ $$$$\mathrm{or}\:\mathrm{downwards}\:\mathrm{along}\:\mathrm{the}\:\mathrm{lines}\:\mathrm{of}\:\mathrm{the} \\…

The-total-number-of-non-similar-triangles-which-can-be-formed-such-that-all-the-angles-of-the-triangle-are-integers-is-

Question Number 22040 by Tinkutara last updated on 10/Oct/17 $$\mathrm{The}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of}\:\mathrm{non}-\mathrm{similar} \\ $$$$\mathrm{triangles}\:\mathrm{which}\:\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{all}\:\mathrm{the}\:\mathrm{angles}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{are} \\ $$$$\mathrm{integers}\:\mathrm{is} \\ $$ Commented by mrW1 last updated on 01/Jan/18…

The-symbols-are-placed-in-the-squares-of-the-adjoining-figure-The-number-of-ways-of-placing-symbols-so-that-no-row-remains-empty-is-

Question Number 22038 by Tinkutara last updated on 10/Oct/17 $$\mathrm{The}\:\mathrm{symbols}\:+,\:+,\:×,\:×,\:\bigstar,\:\bullet,\:\mathrm{are} \\ $$$$\mathrm{placed}\:\mathrm{in}\:\mathrm{the}\:\mathrm{squares}\:\mathrm{of}\:\mathrm{the}\:\mathrm{adjoining} \\ $$$$\mathrm{figure}.\:\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{of}\:\mathrm{placing} \\ $$$$\mathrm{symbols}\:\mathrm{so}\:\mathrm{that}\:\mathrm{no}\:\mathrm{row}\:\mathrm{remains}\:\mathrm{empty} \\ $$$$\mathrm{is} \\ $$ Commented by Tinkutara last updated…

How-many-5-digit-numbers-from-the-digits-0-1-9-have-i-Strictly-increasing-digits-ii-Strictly-increasing-or-decreasing-digits-iii-Increasing-digits-iv-Increasing-or-decreasing-digit

Question Number 22037 by Tinkutara last updated on 10/Oct/17 $$\mathrm{How}\:\mathrm{many}\:\mathrm{5}-\mathrm{digit}\:\mathrm{numbers}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{digits}\:\left\{\mathrm{0},\:\mathrm{1},\:…..,\:\mathrm{9}\right\}\:\mathrm{have}? \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Strictly}\:\mathrm{increasing}\:\mathrm{digits} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Strictly}\:\mathrm{increasing}\:\mathrm{or}\:\mathrm{decreasing} \\ $$$$\mathrm{digits} \\ $$$$\left(\mathrm{iii}\right)\:\mathrm{Increasing}\:\mathrm{digits} \\ $$$$\left(\mathrm{iv}\right)\:\mathrm{Increasing}\:\mathrm{or}\:\mathrm{decreasing}\:\mathrm{digits} \\ $$ Commented…

The-number-of-five-digits-can-be-made-with-the-digits-1-2-3-each-of-which-can-be-used-atmost-thrice-in-a-number-is-

Question Number 22035 by Tinkutara last updated on 10/Oct/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{five}\:\mathrm{digits}\:\mathrm{can}\:\mathrm{be}\:\mathrm{made} \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{1},\:\mathrm{2},\:\mathrm{3}\:\mathrm{each}\:\mathrm{of}\:\mathrm{which}\:\mathrm{can} \\ $$$$\mathrm{be}\:\mathrm{used}\:\mathrm{atmost}\:\mathrm{thrice}\:\mathrm{in}\:\mathrm{a}\:\mathrm{number}\:\mathrm{is} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

2n-objects-of-each-of-three-kinds-are-given-to-two-persons-so-that-each-person-gets-3n-objects-Prove-that-this-can-be-done-in-3n-2-3n-1-ways-

Question Number 22036 by Tinkutara last updated on 14/Oct/17 $$\mathrm{2}{n}\:\mathrm{objects}\:\mathrm{of}\:\mathrm{each}\:\mathrm{of}\:\mathrm{three}\:\mathrm{kinds}\:\mathrm{are} \\ $$$$\mathrm{given}\:\mathrm{to}\:\mathrm{two}\:\mathrm{persons},\:\mathrm{so}\:\mathrm{that}\:\mathrm{each} \\ $$$$\mathrm{person}\:\mathrm{gets}\:\mathrm{3}{n}\:\mathrm{objects}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{this}\:\mathrm{can}\:\mathrm{be}\:\mathrm{done}\:\mathrm{in}\:\mathrm{3}{n}^{\mathrm{2}} \:+\:\mathrm{3}{n}\:+\:\mathrm{1}\:\mathrm{ways}. \\ $$ Commented by Tinkutara last updated on…

Question-153057

Question Number 153057 by DELETED last updated on 04/Sep/21 Answered by DELETED last updated on 04/Sep/21 $$\mathrm{i}_{\mathrm{1}} +\mathrm{i}_{\mathrm{2}} =\mathrm{i}_{\mathrm{3}} \:…..\left(\mathrm{1}\right) \\ $$$$\Sigma\mathrm{E}+\Sigma\mathrm{i}.\mathrm{R}=\mathrm{0}\:\:\mathrm{hk}\:\mathrm{kirchoff}\:\mathrm{II} \\ $$$$\mathrm{loop}\:\mathrm{1}\:\left(\mathrm{searah}\:\mathrm{jarum}\:\mathrm{jam}\right) \\…

Let-n-be-the-number-of-ways-in-which-5-boys-and-5-girls-stand-in-a-queue-in-such-a-way-that-all-the-girls-stand-consecutively-in-the-queue-Let-m-be-the-number-of-ways-in-which-5-boys-and-5-girls-can-

Question Number 21977 by Tinkutara last updated on 08/Oct/17 $$\mathrm{Let}\:{n}\:\mathrm{be}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which} \\ $$$$\mathrm{5}\:\mathrm{boys}\:\mathrm{and}\:\mathrm{5}\:\mathrm{girls}\:\mathrm{stand}\:\mathrm{in}\:\mathrm{a}\:\mathrm{queue}\:\mathrm{in} \\ $$$$\mathrm{such}\:\mathrm{a}\:\mathrm{way}\:\mathrm{that}\:\mathrm{all}\:\mathrm{the}\:\mathrm{girls}\:\mathrm{stand} \\ $$$$\mathrm{consecutively}\:\mathrm{in}\:\mathrm{the}\:\mathrm{queue}.\:\mathrm{Let}\:\mathrm{m}\:\mathrm{be} \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which}\:\mathrm{5}\:\mathrm{boys} \\ $$$$\mathrm{and}\:\mathrm{5}\:\mathrm{girls}\:\mathrm{can}\:\mathrm{stand}\:\mathrm{in}\:\mathrm{a}\:\mathrm{queue}\:\mathrm{in}\:\mathrm{such} \\ $$$$\mathrm{a}\:\mathrm{way}\:\mathrm{that}\:\mathrm{exactly}\:\mathrm{four}\:\mathrm{girls}\:\mathrm{stand} \\ $$$$\mathrm{consecutively}\:\mathrm{in}\:\mathrm{the}\:\mathrm{queue}.\:\mathrm{Then}\:\mathrm{the} \\…

Let-n-1-lt-n-2-lt-n-3-lt-n-4-lt-n-5-be-positive-integers-such-that-n-1-n-2-n-3-n-4-n-5-20-Then-the-number-of-such-distinct-arrangements-n-1-n-2-n-3-n-4-n-5-is-

Question Number 21933 by Tinkutara last updated on 07/Oct/17 $$\mathrm{Let}\:{n}_{\mathrm{1}} \:<\:{n}_{\mathrm{2}} \:<\:{n}_{\mathrm{3}} \:<\:{n}_{\mathrm{4}} \:<\:{n}_{\mathrm{5}} \:\mathrm{be}\:\mathrm{positive} \\ $$$$\mathrm{integers}\:\mathrm{such}\:\mathrm{that}\:{n}_{\mathrm{1}} \:+\:{n}_{\mathrm{2}} \:+\:{n}_{\mathrm{3}} \:+\:{n}_{\mathrm{4}} \:+ \\ $$$${n}_{\mathrm{5}} \:=\:\mathrm{20}.\:\mathrm{Then}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{such} \\…