# 5 indians and 5 american couples meet at aparty and shake hands. if no wife shakes hands with her own husband and no indian wife shakes hands with a male, then the no. of hand shakes that take place in the party is?

148 Points
14 years ago

Dear jee

total possible hand shake =20C2

indian women shake hand with male =5C1 *10C1 =50  ways (it include hand shake with her husband also)

american women shake hand with their husband in 5 ways

so desired hand shake = 20C2 -50-5

=135

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Shashwat Sinha
36 Points
8 years ago
I did it this way and got 95 as the answer.

1 Indian male would shake hands with 5 American males so total no of handshakes between Indian and American males = 25 (5*5)
1 Indian female would shake hands with 5 American females , so number of handshakes = 25
1 American male would shake hands with 4 American females , so total = 20 (5*4)
1 American female would shake hands with 5 Indian males , so total = 25
(can u guys tell me where am i going wrong)
Vanshika bhalla
11 Points
7 years ago
I havent counted hanshakes among indian women and american ones that is...one indian women will shake hands with rest of 4 so total of 5 women will lead to 5*4=20 hamdshakes samr case with american women they will also lead to 20 both adding upto 40 and giving answer 95+40= 135 handshakes
SMITAL LUNAWAT
11 Points
6 years ago
20C2 (total handshakes) - THE NO OF HAND SHAKES OF INDIAN WOMEN WITH MALES i.e. 5C1 X 10C- 5(handshakes of american males with their own wife). which if finally equal to 10C2 – 5C1X10C1 –
5=135