Question

There are 7 persons in a party. The
number of hands shaken all together
in the party counted with multipli
city, cannot be :​

Answer 1

Answer: Say we have

N

people in the room. So to shake hands we have to pair each one of these

N

with each one of the

r

e

s

t

of people in the room. So we have

N

⋅

(

N

−

1

)

possible pairings.

However, in this number we have actually counted each pairing twice; when, say

p

e

r

s

o

n

1

shakes hands with

p

e

r

s

o

n

2

, and when

p

e

r

s

o

n

2

shakes hands with

p

e

r

s

o

n

1

. It is only one handshake.

Thus, the correct number is half of that

N⋅( N−1)/2

Therefore number of hand shake =7(6)/2= 42/2= 21