Distinct Subsequences

Given a string S and a string T, count the number of distinct subsequences of T in S.

A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (ie, "ACE" is a subsequence of "ABCDE"while "AEC" is not).

Here is an example:
S = "rabbbit", T = "rabbit"

Return 3.

public class Solution {
    public int numDistinct(String S, String T) {
        if (S==null || T==null || S.length()<T.length() || (S.length() == T.length() && !S.equals(T)))
            return 0;
        int counter = 0;
        char[] s = S.toCharArray();
        char[] t = T.toCharArray();
        return loopAndMatch(s, 0, t, 0);       
        
    }
    
    public int loopAndMatch(char[] s, int start, char[] t, int index) {
        if (start >= s.length || index >= t.length) {
            return 0;
        }
        int counter = 0;
        char target = t[index];
        for (int i=start; i<s.length; i++) {
            if (s[i]==target) {
                if (index == t.length-1)
                    counter++;
                else 
                    counter += loopAndMatch(s, i+1, t, index+1);
            }
        }
        return counter;
    }
}