# Moderate Permutation-Combination Solved QuestionAptitude Discussion

 Q. There are 20 couples in a party. Every person greets every person except his or her spouse. People of the same sex shake hands and those of opposite sex greet each other with a namaskar (It means bringing one's own palms together and raising them to the chest level). What is the total number of handshakes and namaskar's in the party?
 ✖ A. $760$ ✔ B. $1,140$ ✖ C. $780$ ✖ D. $720$

Solution:
Option(B) is correct

There are 20 men and 20 women.

When a man meets a woman, there are two namaskars, whereas when a man meets a man (or a woman) there is only 1 handshake.

Number of handshakes $= 2\times {^{20}C_2}$ (men and women ) $= 2 \times \dfrac{20 \times 19}{2}=380$

For number of Namskars Every man does 19 namaskars (to the 20 women excluding his wife) and they respond in the same way.

$= 2\times (20)(19)$

$= 2\times 380$

$=760$

Total,

$= 760 + 380$

$= \textbf{1140}$

Edit: Thank you meghna for pointing our the error in the solution. Solution has been updated.

## (6) Comment(s)

Tejas Patil
()

in ur explanation u havent consider women greeting women (they fall under category of same sex) as stated in question.

solution:

same sex greetings(HANDSHAKES)

case1 : man greeting man / handshakes

20c2= 380

case2 : women greeting women / handshakes

20c2=380

case 3: a male can greet 19 female and viceversa.

so, total no of greetings= 20*19=380

now, if u consider ONE greetings equal to TWO namskars i.e. one bye each sex

thanks.

Meghna
()

$^{20}C_2$ is given as $380$. Number of namaskars has to be doubled.

Though the answer is correct there is a mistake in the derivation.

Deepak
()

Thank you Meghna for pointing out the error, solution has been corrected. Hope this is okay now.

Manu Mathur
()

Total handshakes(men and women) $=2*^{20}c_2=380$

Total namaskar $=20*19=380$

Balaji
()

Guess the answer is 780, because handshakes $=2*^{20}C_2=380$ and namaskaar $=20*20=400$.

So,in total $400+380=780$.

Ankit
()

the solution here i think is wrong

as there will be :

$2(19 *20)$ handshakes for men and woman (between same sex)

and $19 *20$ namaskar between men and woman..

so $2*380 +380 = 1140$