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