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…
Question Number 134798 by bramlexs22 last updated on 07/Mar/21 $$\mathrm{Binomial}\:\mathrm{theorem} \\ $$Given that the coefficient of x^2 in the expansion of (1+ax) (3-2 x) ^5…
Question Number 134644 by matthewagushi40 last updated on 06/Mar/21 Commented by mr W last updated on 06/Mar/21 $${please}\:{check}\:{your}\:{typos}!\:{only}\:{correctly} \\ $$$${written}\:{questions}\:{may}\:{get}\:{desired} \\ $$$${answers}! \\ $$ Answered…
Question Number 68947 by Cmr 237 last updated on 20/Oct/19 $$\mathrm{please} \\ $$$$\mathrm{utilise}\:\mathrm{cette}\:\mathrm{fonction}\:\mathrm{to}\: \\ $$$$\mathrm{sh}\boldsymbol{\mathrm{ow}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{N}}\ast\boldsymbol{\mathrm{N}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{denombrable}} \\ $$$$\:\mathrm{f}:\boldsymbol{\mathrm{N}}\circledast\boldsymbol{\mathrm{N}}\rightarrow\boldsymbol{\mathrm{N}} \\ $$$$\:\:\:\:\left(\mathrm{x},\mathrm{y}\right)\shortmid\rightarrow\frac{\left(\mathrm{x}+\mathrm{y}\right)\left(\mathrm{x}+\mathrm{y}+\mathrm{1}\right)}{\mathrm{2}}+\mathrm{y} \\ $$$$\mathrm{montrer}\:\mathrm{que}\:\mathrm{f}\:\mathrm{est}\:\mathrm{bijective} \\ $$$$\:\:\:\boldsymbol{\mathrm{P}}\mathrm{lease}\:\mathrm{help} \\ $$$$…
Question Number 134482 by benjo_mathlover last updated on 04/Mar/21 $$ \\ $$How many ways can this be done if you distribute 25 identical pieces of…
Question Number 134389 by EDWIN88 last updated on 03/Mar/21 $$\mathrm{Eight}\:\mathrm{dice}\:\mathrm{are}\:\mathrm{tossed}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{dice}\:\mathrm{are}\:\mathrm{identical}\:\mathrm{in} \\ $$$$\mathrm{appearance}\:,\:\mathrm{how}\:\mathrm{many}\:\mathrm{different}−\mathrm{looking}\: \\ $$$$\left(\mathrm{distinguishable}\right)\:\mathrm{occurrences}\:\mathrm{are}\:\mathrm{there}? \\ $$ Answered by bramlexs22 last updated on 03/Mar/21 $$\mathrm{Theorem}\: \\…
Question Number 3274 by Yozzi last updated on 09/Dec/15 $${I}\:{have}\:\mathrm{25}\:{horses}\:{and}\:{I}'{d}\:{like}\:{to} \\ $$$${know}\:{which}\:{are}\:{the}\:{three}\:{fastest} \\ $$$${horses}\:{among}\:{them}.\:{I}\:{do}\:{not}\:{have}\:{a} \\ $$$${clock}\:{but}\:{I}\:{have}\:{a}\:{race}\:{track}\:{which} \\ $$$${can}\:{be}\:{used}\:{by}\:\mathrm{5}\:{horses}\:{at}\:{a}\:{time}. \\ $$$${If}\:{each}\:{horse}\:{covers}\:{the}\:{distance} \\ $$$${of}\:{the}\:{track}\:{in}\:{the}\:{same}\:{time}\:{for} \\ $$$${every}\:{race}\:{it}\:{runs},\:{find}\:{the}\:{least} \\…
Question Number 3273 by Yozzi last updated on 09/Dec/15 $$\ast\:\:\ast\:\:\ast\:\:\ast\:\:\:\:{One}\:{can}\:{only}\:{move}\:{to}\:{the} \\ $$$$\ast\:\:\ast\:\:\ast\:\:\ast\:\:\:\:{right}\:{or}\:{downwards}\:{on}\:{the} \\ $$$$\ast\:\:\ast\:\:\ast\:\:\ast\:\:\:\:\mathrm{4}\:{by}\:\mathrm{6}\:{point}\:{lattice}\:{shown}. \\ $$$$\ast\:\:\ast\:\:\ast\:\:\ast\:\:\:\:{How}\:{many}\:{paths}\:{from}\:\ast\:{to} \\ $$$$\ast\:\:\ast\:\:\ast\:\:\ast\:\:\:\:\:\:\ast\:{are}\:{there}?\: \\ $$$$\ast\:\:\ast\:\:\ast\:\:\ast \\ $$$$ \\ $$ Answered…