Question Number 54286 by Tinkutara last updated on 01/Feb/19 Commented by Tinkutara last updated on 01/Feb/19 Answers 4d 5b Commented by mr W last updated on 05/Feb/19…
Question Number 185350 by cortano1 last updated on 20/Jan/23 $$\:\:\:{C}_{\mathrm{4}} ^{\mathrm{4}} +{C}_{\mathrm{4}} ^{\mathrm{5}} +{C}_{\mathrm{4}} ^{\mathrm{6}} +…+{C}_{\mathrm{4}} ^{\mathrm{26}} \:=? \\ $$ Commented by mr W last…
Question Number 119747 by benjo_mathlover last updated on 26/Oct/20 $${Suppose}\:{that}\:\mathrm{7}\:{blue}\:{balls}\:,\:\mathrm{8}\:{red}\:{balls}\:{and}\:\mathrm{9}\:{green} \\ $$$${balls}\:{should}\:{be}\:{put}\:{into}\:{three}\:{boxes}\:{labeled} \\ $$$$\mathrm{1},\mathrm{2}\:{and}\:\mathrm{3},\:{so}\:{that}\:{any}\:{box}\:{contains}\:{at}\:{least} \\ $$$${one}\:{balls}\:{of}\:{each}\:{colour}.\:{How}\:{many}\:{ways} \\ $$$${can}\:{this}\:{arrangement}\:{be}\:{done}? \\ $$ Answered by mr W last…
Question Number 119733 by bemath last updated on 26/Oct/20 Commented by bemath last updated on 26/Oct/20 $${many}\:{choices}\:{of}\:{a}\:{person}'{s}\:{path} \\ $$$${from}\:{A}\:{to}\:{B} \\ $$ Commented by MJS_new last…
Question Number 119479 by 675480065 last updated on 24/Oct/20 $$\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\prod}}\mathrm{cos}\left(\frac{\mathrm{x}}{\mathrm{2}^{\mathrm{k}} }\right)\:=\:? \\ $$ Answered by Olaf last updated on 25/Oct/20 $$\mathrm{sin2}\theta\:=\:\mathrm{2sin}\theta\mathrm{cos}\theta \\ $$$$\mathrm{cos}\theta\:=\:\frac{\mathrm{1}}{\mathrm{2}}.\frac{\mathrm{sin2}\theta}{\mathrm{sin}\theta},\:\theta\:\neq\:{k}\pi…
Question Number 119397 by bemath last updated on 24/Oct/20 $${Find}\:{the}\:{number}\:{of}\:{possible}\:{arrangements} \\ $$$${of}\:{the}\:{letters}\:{in}\:{the}\:{word}\:{PENCILS}\:{if} \\ $$$$\left({a}\right)\:'{E}'\:{is}\:{next}\:{to}\:'{I}' \\ $$$$\left({b}\right)\:{E}\:{comes}\:{before}\:{I} \\ $$$$\left({c}\right)\:{there}\:{are}\:{three}\:{letters}\:{between}\:{E}\:{and}\:{I} \\ $$ Commented by liberty last updated…
Question Number 119390 by mr W last updated on 24/Oct/20 $${we}\:{have}\:\mathrm{15}\:{different}\:{mathematics} \\ $$$${books},\:\mathrm{10}\:{different}\:{physics}\:{books}\:{and} \\ $$$$\mathrm{12}\:{different}\:{chemistry}\:{books}.\:{we}\:{should} \\ $$$${choose}\:\mathrm{6}\:{books}\:{such}\:{that}\:{they}\:{contain} \\ $$$${all}\:{three}\:{kinds}\:{of}\:{books}. \\ $$$${in}\:{how}\:{many}\:{ways}\:{can}\:{we}\:{do}\:{this}? \\ $$ Answered by…
Question Number 119364 by bobhans last updated on 24/Oct/20 $${Suppose}\:{once}\:{more}\:{we}'{re}\:{asked}\: \\ $$$${to}\:{choose}\:{four}\:{students}\:{from}\:{high}\:{school} \\ $$$${class}\:{of}\:\mathrm{15}\:{to}\:{form}\:{a}\:{committee} \\ $$$${but}\:{this}\:{time}\:{we}\:{have}\:{a}\:{restriction} \\ $$$$:\:{we}\:{don}'{t}\:{want}\:{to}\:{committee}\:{to} \\ $$$${consist}\:{of}\:{all}\:{seniors}\:{or}\:{all}\:{juniors} \\ $$$$.{suppose}\:{there}\:{are}\:{eight}\:{seniors} \\ $$$${and}\:{seven}\:{juniors}\:{in}\:{the}\:{class}.\:{How}\:{many} \\…
Question Number 118822 by Don08q last updated on 20/Oct/20 $$\:\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{of}\: \\ $$$$\:\mathrm{the}\:\mathrm{word}\:{LEVITATE}\:\mathrm{be}\:\mathrm{arranged}\:\mathrm{if} \\ $$$$\:\mathrm{the}\:\mathrm{vowels}\:\mathrm{must}\:\mathrm{not}\:\mathrm{be}\:\mathrm{next}\:\mathrm{to}\:\mathrm{each} \\ $$$$\:\mathrm{other} \\ $$ Answered by benjo_mathlover last updated on 20/Oct/20…
Question Number 118694 by benjo_mathlover last updated on 19/Oct/20 $${How}\:{many}\:{sets}\:{of}\:\mathrm{3}\:{numbers}\:{each}\:{can} \\ $$$${be}\:{formed}\:{from}\:{the}\:{numbers}\:\left\{\:\mathrm{1},\mathrm{2},\mathrm{3},…,\mathrm{20}\:\right\}\:{if}\:{no} \\ $$$${two}\:{consecutive}\:{numbers}\:{are}\:{to}\:{be}\:{in}\:{a}\:{set}\:? \\ $$ Answered by bemath last updated on 19/Oct/20 $$\Rightarrow\:\begin{pmatrix}{\mathrm{18}}\\{\:\:\mathrm{3}}\end{pmatrix}\:=\:\frac{\mathrm{18}×\mathrm{17}×\mathrm{16}}{\mathrm{3}×\mathrm{2}×\mathrm{1}}\:=\:\mathrm{3}×\mathrm{17}×\mathrm{16}=\mathrm{816} \\…