Category: Permutation and Combination

Question Number 163313 by SLVR last updated on 06/Jan/22 $$Findthenonnegativeinteger$$$$solutionsof2x+3y+5z=60$$ Answered by mr W last updated on 06/Jan/22 $$let2x+3y=5u$$$$\mathrm{5}{u}+\mathrm{5}{z}=\mathrm{60}…

Question Number 163263 by Ar Brandon last updated on 05/Jan/22 Answered by qaz last updated on 05/Jan/22 $$\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{k}} \mathrm{k}$$\left(\begin{array}{c}\mathrm{n}\\ \mathrm{k}\end{array}\right)$$=\frac{\partial}{\partial\mathrm{x}}\mid_{\mathrm{x}=\mathrm{1}} \left(\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}$$\left(\begin{array}{c}\mathrm{n}\\ \mathrm{k}\end{array}\right)$$\left(−\mathrm{x}\right)^{\mathrm{k}} −\mathrm{1}\right)=\frac{\partial}{\partial\mathrm{x}}\mid_{\mathrm{x}=\mathrm{1}}…

Question Number 97600 by Power last updated on 08/Jun/20 Answered by mahdi last updated on 08/Jun/20 $$19\mathrm{trangles}$$$$3,4,5\mathrm{\&}3,4,6\mathrm{\&}4,5,6\mathrm{\&}3,5,6$$$$3,3,4\mathrm{\&}3,3,5\mathrm{\&}4,4,3\mathrm{\&}4,4,5\mathrm{\&}4,4,6$$$$5,5,3\mathrm{\&}5,5,4\mathrm{\&}5,5,6\mathrm{\&}6,6,3\mathrm{\&}6,6,4\mathrm{\&}6,6,5$$$$\mathrm{3},\mathrm{3},\mathrm{3}\:\&\:\mathrm{4},\mathrm{4},\mathrm{4}\:\&\:\mathrm{5},\mathrm{5},\mathrm{5}\:\&\:\mathrm{6},\mathrm{6},\mathrm{6}…

Question Number 31714 by gunawan last updated on 13/Mar/18 $$\mathrm{Prove}\mathrm{that}$$$$\underset{1}{\sum ^{n-2}}k\left(\begin{array}{c}n-2\\ k\end{array}\right)\left(\begin{array}{c}n+2\\ k+2\end{array}\right)=(n-2)\left(\begin{array}{c}2n-1\\ n-1\end{array}\right)$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 97045 by john santu last updated on 06/Jun/20 $$\mathrm{a}\mathrm{committee}\mathrm{consisting}\mathrm{of}$$$$5\mathrm{men}\mathrm{\&}4\mathrm{women}\mathrm{is}\mathrm{to}\mathrm{be}$$$$\mathrm{chosen}\mathrm{from}8\mathrm{men}\mathrm{\&}4\mathrm{women}.$$$$\mathrm{If}\mathrm{one}\mathrm{man}\mathrm{\&}\mathrm{one}\mathrm{woman}\mathrm{are}\mathrm{husband}$$$$\mathrm{\&}\mathrm{wife},\mathrm{how}\mathrm{many}\mathrm{ways}\mathrm{can}$$$$\mathrm{the}\mathrm{committee}\mathrm{be}\mathrm{chosen}\mathrm{if}$$$$\mathrm{only}\mathrm{one}\mathrm{of}\mathrm{the}\mathrm{husband}\mathrm{\&}\mathrm{wife}$$$$\mathrm{must}\:\mathrm{be}\:\mathrm{chosen}\:?…