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Category: Permutation and Combination

Find-the-number-of-subsets-of-1-2-3-2000-the-sum-of-whose-elements-is-divisible-by-5-

Question Number 120090 by bramlexs22 last updated on 29/Oct/20 $${Find}\:{the}\:{number}\:{of}\:{subsets}\:{of} \\ $$$$\left\{\:\mathrm{1},\mathrm{2},\mathrm{3},…,\mathrm{2000}\:\right\}\:{the}\:{sum}\:{of}\: \\ $$$${whose}\:{elements}\:{is}\:{divisible}\:{by}\:\mathrm{5} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Suppose-that-7-blue-balls-8-red-balls-and-9-green-balls-should-be-put-into-three-boxes-labeled-1-2-and-3-so-that-any-box-contains-at-least-one-balls-of-each-colour-How-many-ways-can-this-arrangeme

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…

k-1-cos-x-2-k-

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…

Find-the-number-of-possible-arrangements-of-the-letters-in-the-word-PENCILS-if-a-E-is-next-to-I-b-E-comes-before-I-c-there-are-three-letters-between-E-and-I-

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…

we-have-15-different-mathematics-books-10-different-physics-books-and-12-different-chemistry-books-we-should-choose-6-books-such-that-they-contain-all-three-kinds-of-books-in-how-many-ways-can-we-d

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…

Suppose-once-more-we-re-asked-to-choose-four-students-from-high-school-class-of-15-to-form-a-committee-but-this-time-we-have-a-restriction-we-don-t-want-to-committee-to-consist-of-all-seniors-or-al

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} \\…