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Made easy Test Series

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Five students, Adnam, Beth, Chao, Dan and Edmund are to be arranged in a line. How many such arrangements are possible if Beth is not allowed to stand next to Dan?

Ans given is 72
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Total arrangements possible - 5! = 120 , A,B,C,D,E

Consider arrangments in which beth and dan together , ie consider them as one unit.  A,C,E,|BD| .

Now arrangements possible = 4!*2 = 24*2 = 48  (2 is multiplied as there are 2 ways to arrange the box - |BD| and |DB|)

so now total ways in which they can stand so that B , D are not together = 120 - 48 = 72. 

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