There are 20 couples in a party. Every person greets every person except his or her spouse. People of the same sex shake hands and those of opposite sex greet each other with a Namaste (It means bringing one's own palms together and raising them to the chest level). What is the total number of handshakes and Namaste's in the party?

There are 20 men and 20 women.
When a man meets a woman, there are two Namastes, whereas when a man meets a man (or a woman) there is only 1 handshake.
Number of handshakes,
= 2 × ²⁰C₂ (men and women ) = 2 × 190 = 380

For a number of Namastes, Every man does 19 Namastes (to the 20 women excluding his wife) and they respond in the same way.
Number of Namastes
= 2 × 20 × 19
= 760

Total number of Namastes and Handshake
= 760 + 380
= 1140