Q.
5 Indian & 5 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 -
IH→ Indian husband, Iw→ Indian wife AH→ American husband, Aw→ American wife
Case 1 : Hand shaking occuring between same nationals and same genders (M/F) IH−IH→5C2=10 ways
Similarly for Iw−Iw,Aw−Aw,AH−AH
Total ways 104=40.
Case 2 : All other possible hand shakes
Hence total number of handshakes =(253+40)+(20)=135
Method-II
Total number of handshakes possible 20C2 undesirable handshakes : 10C2+10C1
Hence, Desired ways =20C2−(10C2+10C1)