Question

At a party of married couples, each man shook hand with everyone except his spouse and no handshakes took place between women. If $13$ married couples attended the party the number of handshakes among these $26$ people was

• A. $230$
• B. $22$
• C. $233$
• D. $234$

Answer 1

The correct option is D $234$

A female can handshakes only with all males and except her husband, there will be $13$ handshakes.
Total handshakes by a female is $12\times 13=156$
A male can handshakes with $24$ people except his wife and himself, so total handshakes are $13\times 24$.
But since handshakes between a and b is same as handshakes between b and a.

$⟹$Handshakes has been counted twice.
Total handshakes will be $13\times \frac{(12+24)}{2}=234$

Hence, option 'D' is correct.