Menu Close

Category: Permutation and Combination

In-a-room-containing-N-people-N-gt-3-at-least-one-person-has-not-shaken-hands-with-everyone-else-in-the-room-What-is-the-maximum-number-of-people-in-the-room-that-could-have-shaken-hands-with-ev

Question Number 125460 by john_santu last updated on 11/Dec/20 InaroomcontainingNpeopleN>3,atleastonepersonhasnotshakenhandswitheveryoneelseintheroom.Whatisthemaximumnumberofpeopleintheroomthatcouldhaveshakenhandswitheveryone$${else}?\: \

There-are-12-students-in-a-party-Five-of-them-are-girls-In-how-many-ways-can-these-12-students-be-arranged-in-a-row-if-i-there-are-no-restrictions-ii-the-5-girls-must-be-together-forming-a-b

Question Number 125208 by liberty last updated on 09/Dec/20 Thereare12studentsinaparty.Fiveofthemaregirls.Inhowmanywayscanthese12studentsbearrangedinarowif(i)therearenorestrictions?(ii)the5girlsmustbetogether(formingablock)?(iii)no2girlsareadjacent(iv)betweentwoparticularboysAandB$$\:,\:{there}\:{no}\:{boys}\:{but}\:{exactly}\:\mathrm{3}\:{girls}? \

In-how-many-ways-can-3-men-and-5-women-be-seated-in-a-row-if-3-specific-women-cannot-sit-next-to-each-other-My-solution-arrangements-when-the-3-women-cannot-sit-next-to-eachother-

Question Number 125191 by Don08q last updated on 08/Dec/20 Inhowmanywayscan3menand5womenbeseatedinarowif3specificwomencannotsitnexttoeachother?Mysolution:arrangementswhenthe3womencannotsitnexttoeachother$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\:\mathrm{5}!\:×\:^{\mathrm{6}} {P}_{\mathrm{3}}…