Category: Permutation and Combination

Question Number 21683 by Tinkutara last updated on 30/Sep/17 $$\mathrm{Suppose}{A}_1{A}_2\dots A_{20}\mathrm{is}\mathrm{a}20-\mathrm{sided}\mathrm{regular}$$$$\mathrm{polygon}.\mathrm{How}\mathrm{many}\mathrm{non}-\mathrm{isosceles}$$$$\left(\mathrm{scalene}\right)\mathrm{triangles}\mathrm{can}\mathrm{be}\mathrm{formed}\mathrm{whose}$$$$\mathrm{vertices}\mathrm{are}\mathrm{among}\mathrm{the}\mathrm{vertices}\mathrm{of}\mathrm{the}$$$$\mathrm{polygon}\mathrm{but}\mathrm{whose}\mathrm{sides}\mathrm{are}\mathrm{not}\mathrm{the}$$$$\mathrm{sides}\mathrm{of}\mathrm{the}\mathrm{polygon}?$$…

Question Number 87175 by john santu last updated on 03/Apr/20 $$\mathrm{if}\mathrm{in}\mathrm{the}\mathrm{expansion}\mathrm{of}{(1+\mathrm{x})}^{\mathrm{n}}\mathrm{the}$$$$\mathrm{coefficient}\mathrm{of}{\mathrm{x}}^9\mathrm{is}\mathrm{the}\mathrm{aritmetic}$$$$\mathrm{mean}\mathrm{of}\mathrm{the}\mathrm{coeficients}\mathrm{of}{\mathrm{x}}^8\mathrm{and}$$$${\mathrm{x}}^{10}.\mathrm{find}\mathrm{the}\mathrm{possible}\mathrm{value}$$$$\mathrm{of}\mathrm{n}\mathrm{where}\mathrm{n}\mathrm{is}\mathrm{a}\mathrm{positive}\mathrm{integer}$$…

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…

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

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