Permutation-Combination
Aptitude

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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.

$720$

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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.

Number of Namaskars,

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

$= 2\times 380$

$=760$

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
 ()

PS: 1140 is WRONG answer..

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

# Diffrent sex greetings [NAMASKAR]

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

total no of namaskars= 380*2=760

SO THE FINAL ANSWER IS,

TOTAL HANDSHAKES + NAMASKARS= 1520.

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 $=20*19=380$

so correct answer is 760.



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 $2*380 +380 = 1140$