Pick a random dolly path for your Cinemachine camera. Just attach this to your camera and drag all the paths you want to choose from!

RandomPathPicker.cs

using System.Collections;
using System.Collections.Generic;
using UnityEngine;
using Cinemachine;
public class RandomPathPicker : MonoBehaviour {

    public CinemachinePathBase [] possiblePaths;
	
	void Start () {
        int randomPathNumber = Random.Range(0, possiblePaths.Length);
        CinemachineDollyCart cartScriptRef = GetComponent<CinemachineDollyCart>();
        cartScriptRef.m_Path = possiblePaths[randomPathNumber];
    }
	
	// Update is called once per frame
	void Update () {
		
	}
}