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Category: Permutation and Combination

Four-integers-are-chosen-at-random-from-0-to-9-inclusive-Find-the-probability-that-no-more-than-2-integers-are-the-same-

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…

please-utilise-cette-fonction-to-show-that-N-N-is-denombrable-f-N-N-N-x-y-x-y-x-y-1-2-y-montrer-que-f-est-bijective-Please-help-

Question Number 68947 by Cmr 237 last updated on 20/Oct/19 $$\mathrm{please} \\ $$$$\mathrm{utilise}\:\mathrm{cette}\:\mathrm{fonction}\:\mathrm{to}\: \\ $$$$\mathrm{sh}\boldsymbol{\mathrm{ow}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{N}}\ast\boldsymbol{\mathrm{N}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{denombrable}} \\ $$$$\:\mathrm{f}:\boldsymbol{\mathrm{N}}\circledast\boldsymbol{\mathrm{N}}\rightarrow\boldsymbol{\mathrm{N}} \\ $$$$\:\:\:\:\left(\mathrm{x},\mathrm{y}\right)\shortmid\rightarrow\frac{\left(\mathrm{x}+\mathrm{y}\right)\left(\mathrm{x}+\mathrm{y}+\mathrm{1}\right)}{\mathrm{2}}+\mathrm{y} \\ $$$$\mathrm{montrer}\:\mathrm{que}\:\mathrm{f}\:\mathrm{est}\:\mathrm{bijective} \\ $$$$\:\:\:\boldsymbol{\mathrm{P}}\mathrm{lease}\:\mathrm{help} \\ $$$$…

Eight-dice-are-tossed-If-the-dice-are-identical-in-appearance-how-many-different-looking-distinguishable-occurrences-are-there-

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}\: \\…

I-have-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-5-horses-at-a-time-If-each-horse-covers-the-dis

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} \\…

One-can-only-move-to-the-right-or-downwards-on-the-4-by-6-point-lattice-shown-How-many-paths-from-to-are-there-

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…