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. $95$
• B. $110$
• C. $135$
• D. $150$

Answer 1

The correct option is C $135$

$l_H\to$ Indian husband, $l_W\to$ Indian wife

$A_H\to$ American husband, $A_W\to$ American wife

Case 1 : Hand shaking occuring between same nationals and same genders (M/F)

$l_H-l_H\to {}^5{C}_2\to 10ways$

Similarly for $l_W-l_W,A_W-A_W,A_H-A_H$

Total ways $10\times 4=10$

Case 2 : All other possible hand shakes

Hence total number of handshakes

$=(25\times 3+40)+\left(20\right)=135$