To talk, sing, hum or to make any sound, air passes between the vocal cords in your throat and causes them to vibrate. Air can escape through your mouth and/or nose when you talk. Can you hum with your nose closed? How about with your mouth closed? 
Discover for Yourself
1. Hum a tune with your mouth and nose open.
2. Continue to hum, but close your mouth.
3. Hum with your mouth open, while humming pinch your nose closed with your fingers.
4. With your mouth closed, hum a tune and again pinch your nose closed.
Results
You can hum as long as your mouth and/or your nose is open, but if both are closed you cannot hum.
Why?
When your mouth and nose are closed, the air flow stops. Thus, the vibrations stop and with it sound stops.