Basically I was trying to calculate the time complexity of below solution ,I took this problem from [Bit masking cap problem][1] and understand it very well But unable to calculate the time complexity as recursion is going inside loop

Even my professor didn't get this how to do it?

How can i write recurrence relation for this?

***BIT MASKING***

There are 100 different types of caps each having a unique id from 1 to 100. Also, there are ‘n’ persons each having a collection of a variable number of caps. One day all of these persons decide to go in a party wearing a cap but to look unique they decided that none of them will wear the same type of cap. So, count the total number of arrangements or ways such that none of them is wearing the same type of cap.

Constraints: 1 <= n <= 10 Example:

**What I have tried:**
#include<bits/stdc++.h>
#define MOD 1000000007
using namespace std;
vector<int> capList[101];
int dp[1025][101];
int allmask;
long long int countWaysUtil(int mask, int i)
{
if (mask == allmask) return 1;
if (i > 100) return 0;
if (dp[mask][i] != -1) return dp[mask][i];
long long int ways = countWaysUtil(mask, i+1);
int size = capList[i].size();
for (int j = 0; j < size; j++)
{
if (mask & (1 << capList[i][j])) continue;
else ways += countWaysUtil(mask | (1 << capList[i][j]), i+1);
ways %= MOD;
}
return dp[mask][i] = ways;
}
void countWays(int n)
{
string temp, str;
int x;
getline(cin, str);
for (int i=0; i<n; i++)
{
getline(cin, str);
stringstream ss(str);
while (ss >> temp)
{
stringstream s;
s << temp;
s >> x;
capList[x].push_back(i);
}
}
allmask = (1 << n) - 1;
memset(dp, -1, sizeof dp);
cout << countWaysUtil(0, 1) << endl;
}
int main()
{
int n;
cin >> n;
countWays(n);
return 0;
}

Exact requirement matters to understand what you try to solve.

Bitmasking and Dynamic Programming | Set 1 (Count ways to assign unique cap to every person) - GeeksforGeeks[^]