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Question

# 5 Indian & 5 American couples meet at a party & shake hands. If no wife shakes hands with her husband & no Indian wife shakes hands with a male, then the number of handshakes that takes place in the party is ′m′ then

A
m=135
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B
m is divisible by 5
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C
m is divisible by 7
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D
m is divisible by 3
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Solution

## The correct options are A m=135 B m is divisible by 5 D m is divisible by 3Total couples =10Total people =20Total Number of hand shake =20C2(Every 2 people will house and hand shake)No, husband shake hand with their wife and No Indian wife shake hands with a male⇒ Total hand shakes by indian wives=5×10Total hand shake of husband/ wife in a couple =10Indian husband / wife hand shake is counted in both of the aboveIt is equal to 5⇒ Total resultant hand shakes=20C2−5−10+5=∠20∠2∠18−60+5=20×192−55=190−55=135m=135It is also divisible by 3 and 5.

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