Category: Permutation and Combination

Question Number 154268 by liberty last updated on 16/Sep/21 Commented by mr W last updated on 16/Sep/21 $$\mathrm{8}!=\mathrm{40320} \\ $$ Commented by liberty last updated…

Question Number 153714 by pete last updated on 09/Sep/21 $$\mathrm{How}\:\mathrm{many}\:\mathrm{three}−\mathrm{digit}\:\mathrm{numbers}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{formed}\:\mathrm{using}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{2},\mathrm{3},\mathrm{5},\mathrm{7},\mathrm{8}\:\mathrm{if}\: \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{odd}\:\mathrm{and}\:\mathrm{no}\:\mathrm{digit}\:\mathrm{is}\:\mathrm{repeted}? \\ $$ Answered by EDWIN88 last updated on 09/Sep/21 $$=\:{P}_{\mathrm{1}} ^{\:\mathrm{3}}…

Question Number 22435 by Tinkutara last updated on 18/Oct/17 $${C}_{\mathrm{0}} \:^{\mathrm{2}{n}} {C}_{{n}} −{C}_{\mathrm{1}} \:^{\mathrm{2}{n}−\mathrm{2}} {C}_{{n}} +{C}_{\mathrm{2}} \:^{\mathrm{2}{n}−\mathrm{4}} {C}_{{n}} \:…. \\ $$$$\mathrm{equals}\:\mathrm{to} \\ $$ Terms of…

Question Number 87790 by mathocean1 last updated on 06/Apr/20 $$\mathrm{How}\:\mathrm{many}\:\mathrm{handshakes}\:\mathrm{are}\:\mathrm{exchanged} \\ $$$$\mathrm{betwen}\:\mathrm{27}\:\mathrm{boys}? \\ $$ Answered by TANMAY PANACEA. last updated on 06/Apr/20 $$\mathrm{27}{C}_{\mathrm{2}} \\ $$$$=\frac{\mathrm{27}!}{\mathrm{2}!\mathrm{25}!}=\frac{\mathrm{27}×\mathrm{26}}{\mathrm{2}}=\mathrm{351}…

Question Number 87732 by mathocean1 last updated on 05/Apr/20 $$\mathrm{Solve}\:\mathrm{it}\:\mathrm{in}\:\mathbb{N} \\ $$$$\mathrm{C}_{\mathrm{n}} ^{\mathrm{3}} −\mathrm{C}_{\mathrm{n}} ^{\mathrm{2}} =\mathrm{5}+\frac{\mathrm{n}^{\mathrm{3}} −\mathrm{6n}^{\mathrm{2}} }{\mathrm{6}} \\ $$ Commented by Tony Lin last…