Menu Close

Category: Permutation and Combination

If-n-objects-are-arranged-in-a-row-then-find-the-number-of-ways-of-selecting-three-of-these-objects-so-that-no-two-of-them-are-next-to-each-other-

Question Number 21587 by Tinkutara last updated on 28/Sep/17 $$\mathrm{If}\:{n}\:\mathrm{objects}\:\mathrm{are}\:\mathrm{arranged}\:\mathrm{in}\:\mathrm{a}\:\mathrm{row},\:\mathrm{then} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{of}\:\mathrm{selecting} \\ $$$$\mathrm{three}\:\mathrm{of}\:\mathrm{these}\:\mathrm{objects}\:\mathrm{so}\:\mathrm{that}\:\mathrm{no}\:\mathrm{two}\:\mathrm{of} \\ $$$$\mathrm{them}\:\mathrm{are}\:\mathrm{next}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other}. \\ $$ Commented by mrW1 last updated on 29/Sep/17…

what-is-coefficient-of-t-3-in-the-expanssion-1-t-6-1-t-3-

Question Number 87074 by jagoll last updated on 02/Apr/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{t}^{\mathrm{3}} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{expanssion}\:\left\{\frac{\mathrm{1}−\mathrm{t}^{\mathrm{6}} }{\mathrm{1}−\mathrm{t}}\right\}^{\mathrm{3}} \: \\ $$ Commented by mr W last updated on 02/Apr/20 $${t}^{\mathrm{2}}…

Four-dice-are-rolled-The-number-of-ways-in-which-at-least-one-die-shows-3-is-

Question Number 21405 by Tinkutara last updated on 23/Sep/17 $$\mathrm{Four}\:\mathrm{dice}\:\mathrm{are}\:\mathrm{rolled}.\:\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways} \\ $$$$\mathrm{in}\:\mathrm{which}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{die}\:\mathrm{shows}\:\mathrm{3},\:\mathrm{is} \\ $$ Answered by myintkhaing last updated on 23/Sep/17 $$\mathrm{1}−\left(\frac{\mathrm{5}}{\mathrm{6}}×\frac{\mathrm{5}}{\mathrm{6}}×\frac{\mathrm{5}}{\mathrm{6}}×\frac{\mathrm{5}}{\mathrm{6}}\right)=\frac{\mathrm{671}}{\mathrm{1296}} \\ $$ Commented…

Find-the-number-of-ways-in-which-n-distinct-balls-can-be-put-into-three-boxes-so-that-no-two-boxes-remain-empty-

Question Number 21406 by Tinkutara last updated on 23/Sep/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which}\:{n} \\ $$$$\mathrm{distinct}\:\mathrm{balls}\:\mathrm{can}\:\mathrm{be}\:\mathrm{put}\:\mathrm{into}\:\mathrm{three} \\ $$$$\mathrm{boxes}\:\mathrm{so}\:\mathrm{that}\:\mathrm{no}\:\mathrm{two}\:\mathrm{boxes}\:\mathrm{remain} \\ $$$$\mathrm{empty}. \\ $$ Commented by mrW1 last updated on 06/Oct/17…

Prove-that-6n-is-divisible-by-2-2n-3-n-

Question Number 21404 by Tinkutara last updated on 23/Sep/17 $$\mathrm{Prove}\:\mathrm{that}\:\left(\mathrm{6}{n}\right)!\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{2}^{\mathrm{2}{n}} .\mathrm{3}^{{n}} . \\ $$ Answered by dioph last updated on 23/Sep/17 $$\mathrm{if}\:{n}\:>\:\mathrm{1},\:\mathrm{there}\:\mathrm{are}\:\mathrm{at}\:\mathrm{least}\:\mathrm{3}{n}\:\mathrm{even} \\ $$$$\mathrm{numbers}\:\mathrm{and}\:\mathrm{2}{n}\:\mathrm{multiples}\:\mathrm{of}\:\mathrm{3}\:\mathrm{in} \\…

In-how-many-ways-can-the-letters-of-the-word-PATLIPUTRA-be-arranged-so-that-the-relative-order-of-vowels-are-consonants-do-not-alter-

Question Number 21374 by Tinkutara last updated on 22/Sep/17 $$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{word}\:\mathrm{PATLIPUTRA}\:\mathrm{be}\:\mathrm{arranged},\:\mathrm{so} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{relative}\:\mathrm{order}\:\mathrm{of}\:\mathrm{vowels}\:\mathrm{are} \\ $$$$\mathrm{consonants}\:\mathrm{do}\:\mathrm{not}\:\mathrm{alter}? \\ $$ Commented by mrW1 last updated on 22/Sep/17…