Question

How can I design and algorithm to generate the list of permutations like P(5,2) from the set {0,1,2,3,4}?

Answer 1

I mean: the list: {0,1}, {0,2},{0,3},{0,4}, etc.

Answer 2

Here's a pseudocode. Use whatever language that suits you.
A:={0,1,2,3,4};
for i=0 to 4
for j=0 to 4
if (i!=j) print A(i), A(j)
next
next
There should be 20 lines of output (permutations)