Q. Indian & American couples meet at a party & shake hands. If no wife shakes hands with her own husband & no Indian wife shakes hands with a male, then the number of hand shakes that takes place in the party is -

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Solution:

Indian husband, Indian wife
American husband, American wife
Case 1 : Hand shaking occuring between same nationals and same genders (M/F)

Similarly for
Total ways .
Case 2 : All other possible hand shakes
image
Hence total number of handshakes

Method-II
Total number of handshakes possible undesirable handshakes :
Hence, Desired ways