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

Answer 1

The correct option is C $135$

$5$ Indian & $5$ American couple

total number of person $=20$

$\to$ total possible hand shake = ${}^{20}{C}_2$

$\to$ Indian woman shake hand with male

${=}^5{C}_1{\times }^{10}{C}_1$

$=5\times 10$

= $50$ ways (it included with her husband)

$\to$ American woman's shake hand with their husband

in $5$ ways

$\to$ so, desired hand shake = ${}^{20}{C}_2-50-5$

$=\frac{20\times 19}{2\times 1}-50-5$

$=190-50-5$

$=135$