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Derangements, Arrangement Of Things So That No Elements Appear In Their Original Place (Important for IITJEE)

Sujoy Das

31/01/2018 3 0

"Like if I have 5 tshirts and i want to gift them to my 5 cousins named A,B,C,D,E, so find number of ways in which particular cousin won't get their particular tshirts."

So number of ways:

D(n)=n!(1-1/1!+1/2!-1/3!+.....(-1)^n1/n!))

Where n is number of things which don't go to their original position
here in this question n = 5

So 5!*(1-1/1!+1/2!-1/3!+1/4!-1/5)) = 44 ways in which 5 tshirts won't go to their original position

D(1) = 0

D(2) = 1

D(3) = 2

D(4) = 9

D(5) = 44

D(6) = 265 (( remember these values of Dearangements )).

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