In how many ways can five examination papers | vedclass

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Question

(D) Total number of arrangements of $5$ distinct examination papers is $5! = 5 	imes 4 	imes 3 	imes 2 	imes 1 = 120$.To find the number of ways w

Vedclass · Accepted Answer

$72$

Vedclass · Answer

(D) Total number of arrangements of $5$ distinct examination papers is $5! = 5 	imes 4 	imes 3 	imes 2 	imes 1 = 120$.To find the number of ways where physics and chemistry papers never come together,we first calculate the number of ways they $DO$ come together.Treat the physics and chemistry papers as a single unit. Now,we have $4$ units to arrange (the single unit of physics-chemistry + the remaining $3$ papers),which can be done in $4!$ ways.Within the single unit,the physics and chemistry papers can be arranged in $2!$ ways.Therefore,the number of arrangements where they come together is $4! 	imes 2! = 24 	imes 2 = 48$.The number of ways they never come together is the total arrangements minus the arrangements where they are together: $120 - 48 = 72$.

In how many ways can five examination papers be arranged so that physics and chemistry papers never come together?

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