Category: Permutation and Combination

Question Number 102800 by bramlex last updated on 11/Jul/20 $$\mathrm{There}\mathrm{are}14\mathrm{boys}\mathrm{and}10\mathrm{girls}\mathrm{in}$$$$\mathrm{a}\mathrm{classroom}.\mathrm{The}\mathrm{teacher}\mathrm{wants}$$$$\mathrm{to}\mathrm{form}\mathrm{a}\mathrm{team}\mathrm{of}5\mathrm{students}.$$$$\mathrm{The}\mathrm{team}\mathrm{must}\mathrm{have}\mathrm{a}\mathrm{least}\mathrm{two}$$$$\mathrm{boys}\mathrm{and}\mathrm{two}\mathrm{girls}.\mathrm{Find}\mathrm{the}$$$$\mathrm{number}\mathrm{of}\mathrm{ways}\mathrm{the}\mathrm{team}\mathrm{can}\mathrm{be}$$$$\mathrm{chosen}.$$ Answered…

Question Number 167979 by nadovic last updated on 31/Mar/22 $$3\mathrm{men}\mathrm{and}4\mathrm{women}\mathrm{are}\mathrm{to}\mathrm{sit}\mathrm{on}\mathrm{a}$$$$\mathrm{table}.\mathrm{Calculate}\mathrm{the}\mathrm{number}\mathrm{of}$$$$\mathrm{possible}\mathrm{sitting}\mathrm{arrangements}\mathrm{if}$$$$\left(a\right)\mathrm{they}\mathrm{sit}\mathrm{in}\mathrm{a}\mathrm{row}\mathrm{such}\mathrm{that}\mathrm{the}$$$$\mathrm{men}\mathrm{must}\mathrm{not}\mathrm{sit}\mathrm{next}\mathrm{to}\mathrm{each}$$$$\mathrm{other}.$$$$\left(b\right)\mathrm{they}\mathrm{sit}\mathrm{in}\mathrm{circular}\mathrm{pattern}\mathrm{and}$$$$\:\:\:\:\:\:\:\:\mathrm{the}\:\mathrm{clockwise}\:\mathrm{and}\:\mathrm{anticlockwise} \…

Question Number 36784 by Joel579 last updated on 05/Jun/18 $$\mathrm{Prove}\mathrm{that}$$$$\underset{r=0}{\sum ^n}r{\left(\begin{array}{c}n\\ r\end{array}\right)}^2=n\left(\begin{array}{c}2n-1\\ n-1\end{array}\right)$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 36398 by NECx last updated on 01/Jun/18 $$ConsidertriangleABC.If206$$$$linesaredrawnfromAtoBChow$$$$manytrianglesareformed?$$ Commented by Rasheed.Sindhi last updated on 02/Jun/18 $$\mathrm{207}+\mathrm{206}+…+\mathrm{1}=\frac{\mathrm{207}×\mathrm{208}}{\mathrm{2}}=\mathrm{21528} \…

Question Number 101732 by mr W last updated on 04/Jul/20 $$\mathrm{There}\mathrm{are}10\mathrm{identical}\mathrm{mathematics}$$$$\mathrm{books},7\mathrm{identical}\mathrm{physics}\mathrm{books}$$$$\mathrm{and}5\mathrm{identical}\mathrm{chemistry}\mathrm{books}.$$$$\mathrm{Find}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{ways}\mathrm{to}\mathrm{compile}$$$$\mathrm{the}\mathrm{books}\mathrm{under}\mathrm{the}\mathrm{condition}\mathrm{that}$$$$\mathrm{same}\mathrm{books}\mathrm{are}\mathrm{not}\mathrm{mutually}\mathrm{adjacent}.$$ Commented by…