Question Number 132174 by EDWIN88 last updated on 12/Feb/21 Commented by EDWIN88 last updated on 12/Feb/21 $$\mathrm{old}\:\mathrm{unswered} \\ $$ Commented by mr W last updated…
Question Number 1074 by Yugi last updated on 05/Jun/15 $${Prove}\:{by}\:{induction}\:{the}\:{following}\:{result}\:{where}\:{N}\:{is}\:{a}\:{positive}\:{even}\:{integer}.\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{S}_{\mathrm{1}} ^{\mathrm{2}} +{S}_{\mathrm{2}} ^{\mathrm{2}} =\mathrm{2}^{{N}} \\ $$$${where}\:\:\:\:{S}_{\mathrm{1}} =\underset{{r}=\mathrm{1}} {\overset{\frac{{N}}{\mathrm{2}}+\mathrm{1}} {\sum}}\left(−\mathrm{1}\right)^{{r}−\mathrm{1}} \begin{pmatrix}{{N}}\\{\mathrm{2}\left({r}−\mathrm{1}\right)}\end{pmatrix}\:\:\:\:{and}\:\:\:\:\:\:{S}_{\mathrm{2}} =\underset{{r}=\mathrm{1}} {\overset{{N}/\mathrm{2}} {\sum}}\left(−\mathrm{1}\right)^{{r}+\mathrm{1}}…
Question Number 66549 by aditya@345 last updated on 17/Aug/19 $$\frac{\mathrm{n}^{\mathrm{2}} !}{\left(\mathrm{n}!\right)^{\mathrm{n}} }=\mathrm{natural}\:\mathrm{number}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 131994 by liberty last updated on 10/Feb/21 Commented by liberty last updated on 10/Feb/21 $$\mathrm{old}\:\mathrm{unswered} \\ $$ Answered by EDWIN88 last updated on…
Question Number 921 by 112358 last updated on 24/Apr/15 $${How}\:{many}\:{arrays}\:{of}\:{the}\:{letters} \\ $$$${of}\:{the}\:{word}\:{BELMOPAN}\:{are}\: \\ $$$${possible}\:{if}\:{no}\:{two}\:{vowels}\:{come} \\ $$$${together}? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 911 by 112358 last updated on 22/Apr/15 $${Eight}\:{people}\:{are}\:{seated}\:{around} \\ $$$${a}\:{circular}\:{table}.\:{Each}\:{person} \\ $$$${must}\:{shake}\:{everyone}'{s}\:{hand}\:{but} \\ $$$${they}\:{must}\:{not}\:{shake}\:{hands}\:{with} \\ $$$${the}\:{two}\:{persons}\:{seated}\:{at}\:{their}\:{sides}. \\ $$$${How}\:{many}\:{handshakes}\:{occur}? \\ $$ Answered by prakash…
Question Number 883 by 112358 last updated on 12/Apr/15 $${How}\:{many}\:{even}\:{numbers}\: \\ $$$${between}\:\mathrm{3000}\:{and}\:\mathrm{7000}\:{can}\:{be} \\ $$$${formed}\:{using}\:{the}\:{digits}\: \\ $$$$\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}\:{and}\:\mathrm{8}\:{if}\:{repetition} \\ $$$${of}\:{digits}\:{is}\:{not}\:{allowed}? \\ $$ Answered by prakash jain last…
Question Number 877 by sagarwal last updated on 07/Apr/15 $$\mathrm{An}\:\mathrm{8}×\mathrm{8}\:\mathrm{checkerboard}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{coloured} \\ $$$$\mathrm{with}\:\mathrm{6}\:\mathrm{colors}\:\:\mathrm{in}\:\mathrm{a}\:\mathrm{way}\:\mathrm{that}\:\mathrm{no}\:\mathrm{2}\:\mathrm{adjacent} \\ $$$$\mathrm{cells}\:\left(\mathrm{sharing}\:\mathrm{side}\right)\:\mathrm{have}\:\mathrm{the}\:\mathrm{same}\:\mathrm{color}.\:\mathrm{In}\:\mathrm{how} \\ $$$$\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{it}\:\mathrm{be}\:\mathrm{done}. \\ $$ Commented by 123456 last updated on 12/Apr/15…
Question Number 66262 by peter frank last updated on 11/Aug/19 $$\boldsymbol{{show}}\:\boldsymbol{{that}}\: \\ $$$$\:^{\boldsymbol{{n}}} \boldsymbol{{c}}_{\boldsymbol{{r}}+\mathrm{1}} +^{\boldsymbol{{n}}} \boldsymbol{{c}}_{\boldsymbol{{r}}\:\:} =^{\boldsymbol{{n}}+\mathrm{1}} \boldsymbol{{c}}_{\boldsymbol{{r}}+\mathrm{1}} \\ $$ Commented by mathmax by abdo…
Question Number 131744 by bemath last updated on 08/Feb/21 Answered by liberty last updated on 08/Feb/21 $$=\:\mathrm{C}_{\mathrm{3}} ^{\mathrm{7}} \:=\:\frac{\mathrm{7}.\mathrm{6}.\mathrm{5}}{\mathrm{3}.\mathrm{2}.\mathrm{1}}\:=\:\mathrm{35}\: \\ $$ Terms of Service Privacy…