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Standard XII
Mathematics
Fundamental Principle of Counting
In a party ev...
Question
In a party every person shakes hands with every other person. If there was a total of 105 handshakes in the party, find the number of persons who were present in the party.
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Solution
Let no. of Persons be 'n' then
no. of handshakes
=
n
C
2
⇒
n
C
2
=
105
⇒
n
!
(
n
−
2
)
!
=
210
⇒
n
2
−
n
−
210
=
0
⇒
n
=
15
(
∵
n
>
0
)
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