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Question Number 214595 by malwan last updated on 13/Dec/24

Commented by malwan last updated on 13/Dec/24

$$Isendjpgphoto$$

Commented by malwan last updated on 13/Dec/24

$$butIcantseeithere$$

Commented by Tinku Tara last updated on 13/Dec/24

$$\mathrm{Ok}.\mathrm{Will}\mathrm{check}$$

Commented by malwan last updated on 13/Dec/24

Commented by malwan last updated on 13/Dec/24

$$thisismyquestion$$

Commented by mr W last updated on 13/Dec/24

$$igot$$$$2\times 3!\times (4!-2\times 3!)=144ways$$

Commented by malwan last updated on 13/Dec/24

$$CanyouexplaneitmrW,$$$$please\cancel{⋚}$$

Commented by mr W last updated on 13/Dec/24

$$sinceitisnotaroundtable,we$$$$shoulddefinesomerules.e.g.$$$$followingtwoarrangementsare$$$$seenasidentical.$$

Commented by mr W last updated on 13/Dec/24

Commented by mr W last updated on 13/Dec/24

$$butfollowingtwoarrangements$$$$areseenasdifferent.$$

Commented by mr W last updated on 13/Dec/24

Commented by mr W last updated on 13/Dec/24

$$nowwecantrytosolve.$$$$wehave4evennumbers.theymay$$$$notbeplacedadjacentlytoeach$$$$other.i.e.theyshouldallonthe$$$$cornersorallinthemiddleofeach$$$$side.thereare2possibilities.to$$$$placethe4evennumbersaround$$$$thetablethereare3!ways.now$$$$wecanplacethe4oddnumvers$$$$inthe4bracketsbetweentheeven$$$$numbers.thereare4!ways,butthe$$$$number3maynotbeplacedonthe$$$$leftorrightsideofthenumber6,$$$$sothenumberofvalidwaysis$$$$4!-2\times 3!.$$$$totallythereare$$$$2\times 3!\times (4!-2\times 3!)=144ways.$$

Commented by malwan last updated on 13/Dec/24

$$thankyousomuchsir$$$$⋚$$

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