Question

there are 137 couples in a house warming party thrown by one of the couples a person shakes hand only with those people whom he/she does not know . the host asks everyone in the party how many handshakes has he/she made and gets a different answer each time . with how many people did the host shake hands?

Answer 1

first you write question properly than only we can give answer right

Answer 2

Answer:

There are 20 men and 20 women.

When a man meets a woman, there are two namaskars, whereas when a man meets a man (or a woman) there is only 1 handshake.

Number of handshakes =$2 \times 20C_{2}$ (men and women) = $2 \times 380 = 760$

For number of Namskars Every man does 19 namaskars (to the 20 women excluding his wife) and they respond in the same way.

Number of Namaskars = $(20 \times 19)$ =380

Total = 760 + 380 = 1140