Method to calculate the number of derangements for any given 'n'(length of permutation) : https://en.wikipedia.org/wiki/Derangement
Suppose, for n = 3, the derangements are as follows : -
1 : {3,1,2}
2 : {2,3,1}
(Meaning of derangement : All permutations of {1,2,3} such that no element in the permutation occurs at it's original index )
But , the new problem is : If only first 'k' indices need to be deranged , then how many permutations are possible ?
Example : -
n=2 and k=2 ,
Answer : (3-ways)
1){2,1,3}
2){2,3,1}
3){3,1,2}
