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I'm guessing 'avoiding pallindrome' means the combinations like "ab" "ba" is not sllowed, right??

What do you mean by 'avoiding pallindrome'? Some people post questions with the most confusing descriptions.

This is a typical backtracking problem. Basically to all the permutation of 5 characters.

If my assumption is correct, then I would handle the problem with recursive approach like

pseudo code:

public void ShowAllCombinations(string inputString, string carry, int point)
{
   if (point >= inputString.Length) return;

   for (int i = point; i < inputString.Length; i++)
   {
       string newString = carry == null or empty ? inputString[i] : carry +  inputString[i];
       // Conversion method from char to string is needed here....
       
       print(newString);

       ShowAllCombinations(inputString, newString, point + 1);
   }  
}

Whatever is clear from question looks like we have to print all the subset of the string.

I think instead of 'pallindrome,' OP meant to say 'anagram.'

Write a program to find palindrome. And inverse the condition. If its palindrome skip it.

can we design a hash function which give same hash value if palindrome are passed....
position of char need to be assigned in a different way starting from both ends upto mid point.
like no of char+for each char(ascii of char*position);
eg,

abcde;
edcba;

no of char= 5
ascii =97,98,99,100,101
position=12321

hash value for abcde=5+(97*1+98*2+99*3+100*2+101*1) = 891
hash value for abcde=5+(101*1+100*2+99*3+98*2+99*1) = 891

You could do a bijective mapping to a bitset or array of 1s and zeros.
If String has n characters, there are 2^n possibilities. Write a loop from 1 to 2^n, convert each to binary and then print only those positions that are 1.

just one more way to do it.

print all the subsets one by one and while printing each subset, keep adding them in reversed format in a prefix tree. each time you add a subset, check if its already present.

if it is discard it otherwise, add print and add it to prefix tree in reversed format.

public List<String> combination(char[] c,int i) {
		List<String> l = new ArrayList<String>();
		l.add(String.valueOf(c[i]));
		if(i+1 < c.length){
			List<String> s = combination(c,i+1);
			l.addAll(s);
			for(String st:s){
				l.add(c[i] + st);
			}
		}
		return l;
	}

This is subset problem.
Generate all subsets of a given set.

s("",abcd)
				   /        \
			s(a,bcd)            s("",bcd)
			/        \                   /         \
	             s(ab,cd)       s(ab,d)      s(ac,d)    s(a,d)
                	/    \              /    \           /   \           /    \
                      abcd    abc    abd     ab     acd    ac     ad      a


C ++ CODE

 void RecSubsets(string scanned, string unscanned)
{
     if(unscanned == "")
                  cout<<scanned;
     RecSubsets(scanned+unscanned[0] , unscanned.substr(1);
     RecSubsets(scanned, unscanned.substr(1));
}

import java.util.ArrayList;
import java.util.Collections;
import java.util.List;

public class Powerset {
private String str = "abcde"; // our string
private List<String> list = new ArrayList<>();

public static void main(String[] args) {
Powerset ps = new Powerset();
for (int i = 0; i < ps.str.length(); i++) { // traverse through all
// characters
ps.subs("", i);
}
Collections.sort(ps.list);
System.out.println("List-> " + ps.list + "size-> " + ps.list.size());
}

void subs(String substr, int index) {
String s = "" + str.charAt(index); // very important, create a variable
// on each stack
s = substr + s; // append the subset so far
//System.out.println(s); // print
list.add(s);

for (int i = index + 1; i < str.length(); i++)
subs(s, i); // call recursively

}
}

public class Combination {

	public static void main(String[] args) {
		String str = "abcde";
		String tmp="";
		
		System.out.println("Print all combinations: ");
		for(int i=0; i<str.length(); ++i) {
			tmp += str.charAt(i);
			
			printCombiantion(tmp, str.substring(i+1, str.length()), String.valueOf(str.charAt(i)));
		}
	}
	
	public static void printCombiantion(String s, String t, String indi) {
		System.out.println(indi);
		for(int i=0; i<t.length(); i++) {
			System.out.println(s+t.charAt(i));
		}
	}

}

public class Combinations {
public static void main(String[] args) {
String[] a = "abcde".split("");
for (int x = 0; x < a.length - 1; x++) {
for (int y = x + 1; y < a.length; y++) {
System.out.print(a[x] + a[y] + "--");
}
System.out.println();
}

}
}