Category: Permutation and Combination

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…

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

Question Number 86684 by john santu last updated on 30/Mar/20 $$\mathrm{If}{(1+\mathrm{px}+{\mathrm{qx}}^2)}^8=1+8\mathrm{x}+{52\mathrm{x}}^2+{\mathrm{kx}}^3+\dots$$$$\mathrm{find}\mathrm{p},\mathrm{q}\mathrm{and}\mathrm{k}.$$ Answered by jagoll last updated on…