Category: Permutation and Combination

Question Number 94397 by peter frank last updated on 18/May/20 Answered by mr W last updated on 18/May/20 $${(3x+5)}^{10}$$$$=5^{10}{(1+\frac{3x}{5})}^{10}$$$$=\mathrm{5}^{\mathrm{10}} \underset{{k}=\mathrm{0}}…

Question Number 159715 by cortano last updated on 20/Nov/21 Commented by mr W last updated on 20/Nov/21 $$ifonedraws12balls,theycouldbe$$$$3redones,3greenones,3blacks,$$$$3blueone.ifonedrawsoneballmore,$$$${one}\:{color}\:{must}\:{have}\:\mathrm{4}\:{balls}.\:{so}\:{the} \…

Question Number 159259 by pticantor last updated on 14/Nov/21 $$\mathit{m}\mathit{o}\mathit{n}\mathit{t}\mathit{r}\mathit{e}\mathit{q}\mathit{u}\mathit{e}$$$$\underset{\mathit{k}=0}{\sum ^{\mathit{n}}}{\mathit{C}}_{2\mathit{n}}^{2\mathit{k}}=2^{2\mathit{n}-1}$$ Answered by mr W last updated on…

Question Number 93450 by john santu last updated on 13/May/20 $$\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{coefficient}$$$$\mathrm{of}{\mathrm{x}}^9\mathrm{in}\mathrm{expansion}(1+\mathrm{x})(1+{\mathrm{x}}^2)$$$$(1+{\mathrm{x}}^3)(1+{\mathrm{x}}^4)\times \dots \times (1+{\mathrm{x}}^{100})?$$ Answered by john…

Question Number 27514 by NECx last updated on 08/Jan/18 $$Thepresidentofarepublicwishes$$$$toassignthepremiership,the$$$$vice-premiership,andsixother$$$$cabinetpoststoaselectedgroup$$$$of8,comprisingof6career$$$$diplomatsand2businessmen.If$$$$noneofthebusinessmencanbe$$$${made}\:{premier}\:{or}\:{vice}\:{premier},{in} \…