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Question

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

A
95
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B
110
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C
135
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D
150
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Solution

The correct option is C 135lH→ Indian husband, lW→ Indian wifeAH→ American husband, AW→ American wifeCase 1 : Hand shaking occuring between same nationals and same genders (M/F)lH−lH→5C2→10waysSimilarly for lW−lW,AW−AW,AH−AHTotal ways 10×4=10Case 2 : All other possible hand shakesHence total number of handshakes=(25×3+40)+(20)=135

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