A large hotel receives telephone calls to its switchboard at an average rate of 50 calls per hour according to a Poisson distribution. The switchboard is staffed by three operators, and the service rate for each of the three operators is an average of 20 calls per hour, with exponential service times. Calculate the following performance measures for the switchboard service system:

1. The average utilization of the help desk

2. The probability that there are no calls to the system

3. The average number of calls waiting in line

4. The average time a call spends waiting in line

5. The average time a call spends in the system

6. The average number of calls in the system