Question Number 4164 by Yozzii last updated on 30/Dec/15 Commented by Yozzii last updated on 30/Dec/15 $${Can}\:{anyone}\:{provide}\:{a}\:{well}\:{explained} \\ $$$${proof}\:{of}\:{this}\:{formula}?\:{I}\:{don}'{t} \\ $$$${understand}\:{why}\:{it}\:{works}. \\ $$ Commented by…
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Question Number 135218 by benjo_mathlover last updated on 11/Mar/21 $$\mathrm{Permutation} \\ $$How many ways can 10 men and 7 women sit at a round table…
Question Number 4105 by prakash jain last updated on 28/Dec/15 $$\mathrm{How}\:\mathrm{many}\:\mathrm{distinct}\:\mathrm{ways}\:\mathrm{are}\:\mathrm{there}\:\mathrm{for} \\ $$$$\mathrm{a}\:\mathrm{knight}\:\mathrm{to}\:\mathrm{reach}\:\mathrm{from}\:\mathrm{bottom}\:\mathrm{left}\:\mathrm{corner}\:\mathrm{of} \\ $$$$\mathrm{chessboard}\:\mathrm{to}\:\mathrm{top}\:\mathrm{right}\:\mathrm{corner}. \\ $$$$\left(\mathrm{knight}\:\mathrm{going}\:\mathrm{from}\:\mathrm{square}\:\mathrm{a1}\:\mathrm{to}\:\mathrm{h8}\right). \\ $$ Commented by Filup last updated on…
Question Number 4103 by prakash jain last updated on 28/Dec/15 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{{m}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{{m}} \:\centerdot\left(\mathrm{2}^{{m}} −\mathrm{1}\right)\:\centerdot\:^{{n}} {C}_{{m}} }{{m}}\:\:=\underset{{m}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{{m}} }{{m}} \\ $$ Commented…
Question Number 69572 by Ajao yinka last updated on 25/Sep/19 Answered by mind is power last updated on 25/Sep/19 $${Let}\:{S}_{\mathrm{0}} =\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\left(_{\mathrm{5}{k}} ^{\mathrm{5}{n}} \right)\:\:\:,{S}_{\mathrm{1}}…
Question Number 135024 by mr W last updated on 09/Mar/21 Commented by mr W last updated on 09/Mar/21 $${an}\:{unsolved}\:{old}\:{question} \\ $$ Commented by mr W…
Question Number 3884 by Yozzii last updated on 23/Dec/15 $${Prove}\:{that}\:{there}\:{are}\:\begin{pmatrix}{{n}+{r}−\mathrm{1}}\\{{n}−\mathrm{1}}\end{pmatrix}\: \\ $$$${ways}\:{of}\:{placing}\:{r}\:{identical}\:{objects} \\ $$$${in}\:{n}\:{compartments},\:{where}\:{n}>{r}. \\ $$ Commented by RasheedSindhi last updated on 24/Dec/15 $${Let}\:{r}\:{objects}\:{are}\:{denoted}\:{as}\: \\…
Question Number 3881 by Yozzii last updated on 23/Dec/15 $${Four}\:{integers}\:{are}\:{chosen}\:{at}\:{random} \\ $$$${from}\:\mathrm{0}\:{to}\:\mathrm{9},\:{inclusive}.\:{Find}\:{the} \\ $$$${probability}\:{that}\:{no}\:{more}\:{than} \\ $$$$\mathrm{2}\:{integers}\:{are}\:{the}\:{same}.\: \\ $$$$ \\ $$ Commented by RasheedSindhi last updated…
Question Number 134905 by bramlexs22 last updated on 08/Mar/21 $$\mathrm{Combinatorics} \\ $$What is the number of ways of distributing 9 different objects among 5 persons…