One thousand people in. room decide to shake hands with every other person in the room. Instead of o

One thousand people in. room decide to shake hands with every other person in the room. Instead of one handshake per couple, each person must shake both of the hands of every person in the room with both his right and his left hand. (Tom will use his right hand to shake Dave's right hand and then Dave's left hand. Tom will then use his left hand to shake Dave's right hand and then Dave's left hand.) How many total handshakes will take place?

1000 people taken 2 at a time:
1000C2 = 499,500

But each group of 2 makes 4 unique handshakes:
499,500 * 4 = 1,998,000