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Question

# In a party there are 10 married couples, Each person shakes hands with every person other than her or his spouse. The total number of hand shakes exchanged in that party is ____

A
160
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B
190
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C
180
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D
170
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Solution

## The correct option is C 180There are 10 married couples.Total number of persons =20Each person shakes hands with every person,So, total number of handshakes =20C2A person does not shake hand with their spouse.So, number of handshakes between each couple =10Therefore, total handshakes exchanged in party = 20C2−10=20!2!18!−10=20×192−10=190−10=180The total number of handshakes exchanged in a party is 180.

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