Complete Derangement (Hindi): Theory, Summation & Recursive Formula proof, Application & 5 Examples

Complete Derangement (Hindi): Theory, Formula proof (Summation & Recursive), Application & Examples
Summation formula proof: Dn=n!(1-1/1!+1/2!-1/3!+...+(-1)^n/n!)
Introduction and Recursive relation proof (formula): Dn=(n-1)(Dn-1+Dn-2)
Example 1: In how many ways n people can be deranged into n assigned houses?
Example 2: In how many ways 5 balls can be distributed into 5 boxes so that no ball goes to its same color box?
Example 3: How many one-one functions can be defined from A to A such that f(i) is not equal to i
Example 4: Passage based question in derangement of colored balls and boxes
Example 5: if how many ways we can derange 5 balls in 5 boxes so that no ball goes to its same color box and it is given that blue ball is in red box?

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