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 ${}^{\prime }{m}^{\prime }$ then

• A. $m=135$
• B. $m$ $is$ $divisible$ $by$ $5$
• C. $m$ $is$ $divisible$ $by$ $7$
• D. $m$ $is$ $divisible$ $by$ $3$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $m=135$
B $m$ $is$ $divisible$ $by$ $5$
D $m$ $is$ $divisible$ $by$ $3$

Total couples $=10$

Total people $=20$

Total Number of hand shake ${=}^{20}{C}_2$

(Every $2$ people will house and hand shake)

No, husband shake hand with their wife and No Indian wife shake hands with a male

$\Rightarrow$ Total hand shakes by indian wives

$=5\times 10$

Total hand shake of husband/ wife in a couple $=10$

Indian husband / wife hand shake is counted in both of the above

It is equal to $5$

$\Rightarrow$ Total resultant hand shakes

${=}^{20}{C}_2-5-10+5$

$=\frac{\angle 20}{\angle 2\angle 18}-60+5$

$=\frac{20\times 19}{2}-55$

$=190-55=135$

$m=135$

It is also divisible by $3$ and $5$.