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Category: Permutation and Combination

sir-number-of-3-digit-numbers-which-are-divisible-by-a-3-b-4-c-6-d-7-e-8-f-9-g-11-when-repetetion-is-1-Allowwd-2-Not-allowed-kindly-help-me-sir-

Question Number 197564 by SLVR last updated on 21/Sep/23 $${sir}…{number}\:{of}\:\mathrm{3}\:{digit} \\ $$$${numbers}\:{which}\:{are}\:{divisible} \\ $$$${by}\: \\ $$$$\left.{a}\left.\right)\left.\mathrm{3}\left.\:\left.\:\left.{b}\left.\right)\mathrm{4}\:\:{c}\right)\mathrm{6}\:\:{d}\right)\mathrm{7}\:\:{e}\right)\mathrm{8}\:\:{f}\right)\mathrm{9}\:\:{g}\right)\mathrm{11} \\ $$$${when}\:{repetetion}\:{is} \\ $$$$\left.\mathrm{1}\left.\right){Allowwd}\:\:\mathrm{2}\right){Not}\:{allowed}.. \\ $$$${kindly}\:{help}\:{me}\:{sir} \\ $$ Commented…

f-1-2-x-d-dx-0-x-f-x-t-pit-dt-Prove-that-f-1-2-1-2-f-At-least-for-f-1-then-f-x-

Question Number 196322 by sniper237 last updated on 22/Aug/23 $$\:\:\:\:{f}^{\left(\mathrm{1}/\mathrm{2}\right)} \left({x}\right)=\:\frac{{d}}{{dx}}\left(\int_{\mathrm{0}} ^{{x}} \:\frac{{f}\left({x}−{t}\right)}{\:\sqrt{\pi{t}}}{dt}\right) \\ $$$${Prove}\:\:{that}\:\:\:\:\left({f}^{\left(\mathrm{1}/\mathrm{2}\right)} \right)^{\left(\mathrm{1}/\mathrm{2}\right)} =\:{f}\:'\:\:\:\: \\ $$$${At}\:\:{least}\:\:{for}\:\:{f}\:=\:\:\mathrm{1}\:\:{then}\:\:{f}\:=\:{x} \\ $$ Answered by witcher3 last…

say-you-have-3-different-books-about-mathematics-4-different-books-about-physics-and-5-different-books-about-chemistry-in-how-many-ways-can-you-arrange-them-in-a-shelf-such-that-no-two-books-f

Question Number 196143 by mr W last updated on 18/Aug/23 $${say}\:{you}\:{have}\:\mathrm{3}\:\left({different}\right)\:{books} \\ $$$${about}\:{mathematics},\:\mathrm{4}\:\left({different}\right) \\ $$$${books}\:{about}\:{physics}\:{and}\:\mathrm{5}\:\left({different}\right) \\ $$$${books}\:{about}\:{chemistry}.\:{in}\:{how}\:{many} \\ $$$${ways}\:{can}\:{you}\:{arrange}\:{them}\:{in}\:{a}\:{shelf} \\ $$$${such}\:{that}\:{no}\:{two}\:{books}\:{from}\:{the}\:{same} \\ $$$${subject}\:{are}\:{adjacent}? \\ $$…

the-family-A-has-5-members-and-the-family-B-has-4-members-there-are-6-personsfrom-other-families-in-how-many-ways-can-you-arrange-these-15-persons-around-a-round-table-such-that-no-member-from-fami

Question Number 195964 by mr W last updated on 15/Aug/23 $${the}\:{family}\:{A}\:{has}\:\mathrm{5}\:{members}\:{and}\:{the} \\ $$$${family}\:{B}\:{has}\:\mathrm{4}\:{members}.\:{there}\:{are}\: \\ $$$$\mathrm{6}\:{personsfrom}\:{other}\:{families}. \\ $$$${in}\:{how}\:{many}\:{ways}\:{can}\:{you}\:{arrange} \\ $$$${these}\:\mathrm{15}\:{persons}\:{around}\:{a}\:{round}\:{table} \\ $$$${such}\:{that}\:{no}\:{member}\:{from}\:{family}\:{A} \\ $$$${and}\:{no}\:{member}\:{from}\:{family}\:{B}\:{are} \\ $$$${next}\:{to}\:{each}\:{other}?…

how-many-different-words-can-be-formed-from-the-letters-in-aaacdefgbbbb-such-that-a-a-and-a-b-are-not-next-to-each-other-see-also-Q-195606-

Question Number 195672 by mr W last updated on 07/Aug/23 $${how}\:{many}\:{different}\:{words}\:{can}\:{be} \\ $$$${formed}\:{from}\:{the}\:{letters}\:{in} \\ $$$$\boldsymbol{{aaacdefgbbbb}} \\ $$$${such}\:{that}\:{a}\:“\boldsymbol{{a}}''\:{and}\:{a}\:“\boldsymbol{{b}}''\:{are}\:{not} \\ $$$${next}\:{to}\:{each}\:{other}? \\ $$$$ \\ $$$$\left({see}\:{also}\:{Q}#\mathrm{195606}\right) \\ $$…

sequence-of-string-said-to-be-orderly-if-element-index-i-different-to-i-1-for-example-aba-has-orderly-value-2-abab-has-orderly-value-3-abaabb-has-orderly-value-3-if-there-are-7-a-and-13-b-exa

Question Number 195666 by uchihayahia last updated on 07/Aug/23 $$ \\ $$$$\:{sequence}\:{of}\:{string}\:{said}\:{to}\:{be}\:{orderly} \\ $$$$\:{if}\:{element}\:{index}\:{i}\:{different}\:{to}\:{i}+\mathrm{1} \\ $$$$\:{for}\:{example} \\ $$$$\:{aba}\:{has}\:{orderly}\:{value}\:\mathrm{2} \\ $$$$\:{abab}\:{has}\:{orderly}\:{value}\:\mathrm{3} \\ $$$$\:{abaabb}\:{has}\:{orderly}\:{value}\:\mathrm{3} \\ $$$$\:{if}\:{there}\:{are}\:\mathrm{7}\:{a}\:{and}\:\mathrm{13}\:{b} \\…