# how to generate permutations of N numbers in K positions

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Ali Danish on 19 Feb 2019
Commented: Walter Roberson on 24 Nov 2022 at 3:54
I want to generate all permutations of N numbers in K places, where K is less than N (nPk) in matlab, I've searched online and already existing questions but couldn't find a functions which generates such permutations without repitition. There are some functions which do this with repitation.
For example if I've a vector [1 2 3 4] my N is 4 and my K is 2, then I want 12 permutations using the formula N!/(N-K)1 = 4!/(4-2)! = 12
[1,2]
[1,3]
[1,4]
[2,1]
[2,3]
[2,4]
[3,1]
[3,2]
[3,3]
[4,1]
[4,2]
[4,3]
These are the permutations which I want to generate. Kindly suggest me the solution.

Bruno Luong on 22 Mar 2021
Edited: Bruno Luong on 22 Mar 2021
No loop, no extrenal file needed
N=5; K=3;
P=nchoosek(1:N,K);
P=reshape(P(:,perms(1:K)),[],K)
You might further sort the permutation so that the order is easily to follow
P = sortrows(P)
Walter Roberson on 24 Nov 2022 at 3:54
If you have an array P that is 2 or more dimensions (not a vector!), and you use P(A,B) where A and B might be arrays, then the result is the same as if you had used P(A(:), B(:)) -- so P(A(1),B(1)), P(A(2),B(1)), P(A(3),B(1)) up to P(A(end),B(1)) is the first column, then the second column would be P(A(1),B(2)), P(A(2),B(2)), P(A(3),B(2)) to P(A(end),B(2)), and so on -- all combinations of the elements in A with all of the elements in B, same as if A and B had been vectors rather than 2D arrays.
The shape of the result might be different if P is a vector instead of a 2D array.

Stephen23 on 19 Feb 2019
Edited: Stephen23 on 19 Feb 2019
and use it like this:
>> sortrows(combinator(4,2,'p'))
ans =
1 2
1 3
1 4
2 1
2 3
2 4
3 1
3 2
3 4
4 1
4 2
4 3
If you want to apply this to a vector that is not 1:N, simply use the output of combinator as indices into your vector.

Sergey Kasyanov on 22 Mar 2021
Hello!
Use nchoosek function with combination of perms function. That solution is slow but does not require any side files.
res = nchoosek(1:4, 2);
for i = 1:size(res,1)
res = [res; perms(res(i,:))];
end
res = unique(res, 'rows');

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