Category: Permutation and Combination

Question Number 151615 by pete last updated on 22/Aug/21 $$\mathrm{How}\mathrm{many}\mathrm{numbers}\mathrm{greater}\mathrm{than}200\mathrm{can}$$$$\mathrm{be}\mathrm{formed}\mathrm{from}\mathrm{the}\mathrm{digits}1,2,3,4,5\mathrm{if}\mathrm{no}$$$$\mathrm{digit}\mathrm{is}\mathrm{to}\mathrm{be}\mathrm{repeated}\mathrm{in}\mathrm{any}\mathrm{particular}$$$$\mathrm{number}?$$$$$$ Answered by mr W last…

Question Number 85817 by jagoll last updated on 25/Mar/20 $$\mathrm{what}\mathrm{is}\mathrm{coefficient}\mathrm{of}{\mathrm{x}}^2\mathrm{in}$$$$\mathrm{the}\mathrm{expansion}{\left[(1-\mathrm{x})(1+2\mathrm{x})\right]}^6$$ Answered by john santu last updated on 25/Mar/20 $$\left(\mathrm{1}+{x}−\mathrm{2}{x}^{\mathrm{2}} \right)^{\mathrm{6}\:\:}…

Question Number 150859 by alcohol last updated on 15/Aug/21 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 150554 by pete last updated on 13/Aug/21 $$\mathrm{Show}\mathrm{that}{\mathrm{n}}_{{\mathrm{C}}_{\mathrm{r}}}=\frac{\mathrm{n}(\mathrm{n}-1)(\mathrm{n}-2)\dots (\mathrm{n}-\mathrm{r}+1)}{\mathrm{r}!}$$ Answered by Ar Brandon last updated on 13/Aug/21 $$\frac{n(n-1)(n-2)\dots (n-r+1)}{r!}$$$$=\frac{{n}\left({n}−\mathrm{1}\right)…\left({n}−{r}+\mathrm{1}\right)\left({n}−{r}\right)!}{\left({n}−{r}\right)!{r}!}…

Question Number 84993 by mr W last updated on 18/Mar/20 $$100applesshouldbepackedinthree$$$$boxesandeachboxshouldcontain$$$$atleast10apples.inhowmanyways$$$$canthisbedone?$$ Commented by john santu last updated…