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Category: Permutation and Combination

Question-148835

Question Number 148835 by DELETED last updated on 31/Jul/21 Answered by DELETED last updated on 31/Jul/21 $$\mathrm{Lihat}\:\mathrm{Hambatan}\:\mathrm{Seri}\:\mathrm{satu} \\ $$$$\mathrm{R}_{\mathrm{s1}} =\mathrm{R}_{\mathrm{1}\Omega} +\mathrm{R}_{\mathrm{3}\Omega} +\mathrm{R}_{\mathrm{4}\Omega} \\ $$$$\mathrm{R}_{\mathrm{s1}} =\mathrm{1}+\mathrm{3}+\mathrm{4}=\mathrm{8}\:\Omega…

To-the-member-in-forum-please-give-an-opinion-on-this-matter-George-Lucia-and-12-of-their-friends-will-sit-around-a-round-table-Many-of-their-arrangements-sit-if-George-and-Lucia-always-flank-5

Question Number 82975 by jagoll last updated on 26/Feb/20 $$\mathrm{To}\:\mathrm{the}\:\mathrm{member}\:\mathrm{in}\:\mathrm{forum}.\:\mathrm{please}\: \\ $$$$\mathrm{give}\:\mathrm{an}\:\mathrm{opinion}\:\mathrm{on}\:\mathrm{this}\:\mathrm{matter}. \\ $$$$\mathrm{George}\:,\:\mathrm{Lucia}\:\mathrm{and}\:\mathrm{12}\:\mathrm{of}\:\mathrm{their} \\ $$$$\mathrm{friends}\:\mathrm{will}\:\mathrm{sit}\:\mathrm{around}\:\mathrm{a}\:\mathrm{round}\:\mathrm{table}. \\ $$$$\mathrm{Many}\:\mathrm{of}\:\mathrm{their}\:\mathrm{arrangements}\:\mathrm{sit}\: \\ $$$$\mathrm{if}\:\mathrm{George}\:\mathrm{and}\:\mathrm{Lucia}\:\mathrm{always}\:\mathrm{flank} \\ $$$$\mathrm{5}\:\mathrm{of}\:\mathrm{their}\:\mathrm{friends}? \\ $$ Commented…

Question-148092

Question Number 148092 by puissant last updated on 25/Jul/21 Answered by Olaf_Thorendsen last updated on 25/Jul/21 $$\mathrm{R}\:\mathrm{est}\:\mathrm{le}\:\mathrm{rayon}\:\mathrm{du}\:\mathrm{cercle}. \\ $$$$\mathrm{O}\:\mathrm{est}\:\mathrm{le}\:\mathrm{centre}\:\mathrm{du}\:\mathrm{cercle}. \\ $$$$\mathrm{B}\begin{pmatrix}{\mathrm{R}}\\{\mathrm{R}}\end{pmatrix},\:\mathrm{C}\begin{pmatrix}{\mathrm{R}}\\{\mathrm{R}−\mathrm{15}}\end{pmatrix} \\ $$$$\mathrm{Aire}_{\mathrm{ABC}} \:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{AB}×\mathrm{AC} \\…

In-how-many-ways-can-a-family-of-5-brothers-be-seated-round-a-table-if-i-2-brothers-must-seat-next-to-each-other-ii-2-brothers-must-not-seat-together-

Question Number 16876 by tawa tawa last updated on 27/Jun/17 $$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{a}\:\mathrm{family}\:\mathrm{of}\:\mathrm{5}\:\mathrm{brothers}\:\mathrm{be}\:\mathrm{seated}\:\mathrm{round}\:\mathrm{a}\:\mathrm{table} \\ $$$$\mathrm{if}\:\left(\mathrm{i}\right)\:\mathrm{2}\:\mathrm{brothers}\:\mathrm{must}\:\mathrm{seat}\:\mathrm{next}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{2}\:\mathrm{brothers}\:\mathrm{must}\:\mathrm{not}\:\mathrm{seat}\:\mathrm{together}. \\ $$ Answered by mrW1 last updated on 27/Jun/17 $$\left(\mathrm{i}\right)…

In-how-many-ways-can-the-letters-of-the-word-EVERMORE-be-arrange-if-the-word-must-begin-with-i-R-ii-E-

Question Number 16868 by tawa tawa last updated on 27/Jun/17 $$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{of}\:\mathrm{the}\:\mathrm{word}.\:\mathrm{EVERMORE}\:\mathrm{be}\:\mathrm{arrange} \\ $$$$\mathrm{if}\:\mathrm{the}\:\mathrm{word}\:\mathrm{must}\:\mathrm{begin}\:\mathrm{with}\: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{R} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{E} \\ $$ Answered by mrW1 last updated on…

Find-how-many-number-greater-than-2-500-can-be-formed-from-the-digit-0-1-2-3-4-if-no-digit-can-be-used-more-than-once-

Question Number 16836 by tawa tawa last updated on 26/Jun/17 $$\mathrm{Find}\:\mathrm{how}\:\mathrm{many}\:\mathrm{number}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{2},\mathrm{500}\:\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{from}\:\mathrm{the}\:\mathrm{digit} \\ $$$$\mathrm{0},\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4}\:\:\mathrm{if}\:\mathrm{no}\:\mathrm{digit}\:\mathrm{can}\:\mathrm{be}\:\mathrm{used}\:\mathrm{more}\:\mathrm{than}\:\mathrm{once}. \\ $$ Answered by mrW1 last updated on 27/Jun/17 $$\mathrm{2}×\mathrm{4}×\mathrm{3}×\mathrm{2}=\mathrm{48} \\ $$…

Question-147876

Question Number 147876 by puissant last updated on 24/Jul/21 Answered by Olaf_Thorendsen last updated on 24/Jul/21 $$\mathrm{On}\:\mathrm{raisonne}\:\mathrm{par}\:\mathrm{recurrence}. \\ $$$$ \\ $$$$\mathrm{On}\:\mathrm{considere}\:\mathrm{la}\:\mathrm{propriete}\:\mathrm{suivante}\:: \\ $$$$ \\ $$$$“\mathrm{Si}\:\mathrm{on}\:\mathrm{retire}\:\mathrm{une}\:\mathrm{case}\:\mathrm{quelconque}…