leetcode -- Permutation Sequence

The set [1,2,3,…,n] contains a total of n! unique permutations.

By listing and labeling all of the permutations in order,
We get the following sequence (ie, for n = 3):

1. "123"
2. "132"
3. "213"
4. "231"
5. "312"
6. "321"

 Given n and k, return the k^th permutation sequence.

Note: Given n will be between 1 and 9 inclusive.

public class Solution {
    public String getPermutation(int n, int k) {
        // Start typing your Java solution below
        // DO NOT write main() function
        int[] num = new int[n];
        int count = 1;
        for(int i = 0; i < n; i++){
            num[i] = i + 1;
            count *= (i+1);
        }
        k--;
        StringBuilder sb = new StringBuilder();
        for(int i = 0; i < n; i++){
            count /= n - i;
            int selected = k / count;
            k = k % count;
            //count = count / (n - i - 1);
            
            sb.append(num[selected]);
            for(int j = selected + 1; j < n; j++){
                num[j - 1] = num[j];
            }
        }
        return sb.toString();
    }
}