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
Please feel free to post as many doubts on our discussion forum as you can.
If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.
We are all IITians and here to help you in your IIT JEE  & AIEEE preparation. 
All the best. 
Regards, 
Askiitians Experts 
Badiuddin
										

										
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)
										

										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
										

										
20C2 (total handshakes) - THE NO OF HAND SHAKES OF INDIAN WOMEN WITH MALES i.e. 5C1 X 10C1 - 5(handshakes of american males with their own wife). which if finally equal to 10C2 – 5C1X10C1 – 
5=135