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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 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 1355 Indian & 5 American coupletotal number of person =20→ total possible hand shake = 20C2→ Indian woman shake hand with male=5C1×10C1=5×10= 50 ways (it included with her husband)→ American woman's shake hand with their husbandin 5 ways→ so, desired hand shake = 20C2−50−5=20×192×1−50−5=190−50−5=135

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