------
## 最终结论
```python
def numberOfWays(hats):
    MOD = 10**9 + 7
    n = len(hats)
    
    # dp[mask] will hold the number of ways to assign hats for a given mask
    dp = [0] * (1 << n)
    dp[0] = 1  # There's one way to assign no hats
    
    # Create a mapping from hat to people who like that hat
    hat_to_people = [[] for _ in range(41)]
    
    for person in range(n):
        for hat in hats[person]:
            hat_to_people[hat].append(person)
    
    # Iterate through each hat and update the dp array
    for hat in range(1, 41):
        # We need to iterate backwards to prevent overwriting results we still need to use
        for mask in range((1 << n) - 1, -1, -1):
            if dp[mask] > 0:  # If there are ways to assign hats for this mask
                for person in hat_to_people[hat]:
                    new_mask = mask | (1 << person)  # Assign this hat to the person
                    dp[new_mask] = (dp[new_mask] + dp[mask]) % MOD
    
    return dp[(1 << n) - 1]  # Return the number of ways to assign hats to all people

# Example usage:
hats = [[3,4],[4,5],[5]]
print(numberOfWays(hats))  # Output: 1
```