A,B,C and D have mixed up their respective secret codes in an envelope in How many ways can they pick up their codes in such a manner that no one gets his own code ?

Explanation

Let a,b,c,d respectively represent codes of A,B,C,D when codes a,b,c,d are mixed up they can be picked up in `4!""=24 ` ways
But codes have been picked up so that A does not get a,B does not get b,C does not get c and D does not get d. Hence problem reduces to total number of derangement of a,b,c,d.
`=4![1-(1)/(1!)+(1)/(2!)-(1)/(3!)-(1)/(4!)]`=9