Category: Permutation and Combination

Question Number 187948 by horsebrand11 last updated on 24/Feb/23 $$$$$$\mathrm{Given}\mathrm{a}\mathrm{set}\mathrm{H}=\{1,2,3,\dots ,300.\mathrm{We}\mathrm{will}\mathrm{a}$$$$\mathrm{cre}a\mathrm{te}\mathrm{a}\mathrm{subset}\mathrm{of}\mathrm{H}\mathrm{consisting}\mathrm{of}$$$$\mathrm{thre}e\mathrm{elements}.\mathrm{If}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}$$$$\mathrm{thr}e\mathrm{e}\mathrm{elements}\mathrm{is}\mathrm{divisible}\mathrm{by}3$$$$\mathrm{then}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{subsets}\mathrm{that}$$$$\mathrm{canbe}\mathrm{made}\mathrm{is}\mathrm{x}.\mathrm{Find}\mathrm{the}$$$$\mathrm{remaind}{e}\mathrm{r}\:\mathrm{if}\:\mathrm{x}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{100000} \…

Question Number 56784 by Runzzy last updated on 23/Mar/19 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 122250 by mr W last updated on 15/Nov/20 Answered by mr W last updated on 15/Nov/20 $$usinggeneratingfunctionmethod$$$$thenumberofwaysisthecoefficient$$$${of}\:{term}\:{x}^{\mathrm{10}} \:{in}\:{the}\:{expansion} \…

Question Number 56678 by pieroo last updated on 21/Mar/19 $$\mathrm{A}\mathrm{box}\mathrm{contains}9\mathrm{whites},7\mathrm{red}\mathrm{and}4\mathrm{blue}$$$$\mathrm{balls}.\mathrm{Three}\mathrm{balls}\mathrm{are}\mathrm{picked}\mathrm{at}\mathrm{random},$$$$\mathrm{one}\mathrm{after}\mathrm{the}\mathrm{other}\mathrm{without}\mathrm{replacement}.$$$$\mathrm{a})\mathrm{find}\mathrm{the}\mathrm{probability}\mathrm{that}:$$$$\mathrm{i}.\mathrm{they}\mathrm{are}\mathrm{all}\mathrm{of}\mathrm{the}\mathrm{same}\mathrm{color}$$$$\mathrm{ii}.\mathrm{there}\mathrm{is}\mathrm{one}\mathrm{of}\mathrm{each}\mathrm{colour}$$$$\mathrm{iii}.\mathrm{two}\mathrm{of}\mathrm{them}\mathrm{are}\mathrm{red}$$$$\left.\mathrm{b}\right)\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{known}\:\mathrm{that}\:\mathrm{the}\:\mathrm{first}\:\mathrm{one}\:\mathrm{picked} \…

Question Number 56615 by pieroo last updated on 19/Mar/19 $$\mathrm{In}\mathrm{how}\mathrm{many}\mathrm{different}\mathrm{ways}\mathrm{can}\mathrm{the}$$$$\mathrm{letters}\mathrm{of}\mathrm{the}\mathrm{word}\mathrm{OKINKWO}\mathrm{be}\mathrm{arranged}?$$$$\mathrm{In}\mathrm{how}\mathrm{many}\mathrm{of}\mathrm{these}\mathrm{arrangements}$$$$\mathrm{does}\mathrm{an}\mathrm{O}\mathrm{occupy}\mathrm{both}\mathrm{end}\mathrm{points}\mathrm{of}$$$$\mathrm{the}\mathrm{word}?$$ Commented by mr W last…