Home > Practice > Arithmetic Aptitude > Permutations and Combinations > Miscellaneous
1. 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?
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
Solution:
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