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Question
After a meeting, every participant shakes hands with every other participants. If the number of handshakes is 66, find the number of participants in the meeting.
Solution
Let there be n participants present in the meeting.
A handshake occurs between 2 persons.
∴ Number of handshakes = nC2
Given 66 handshakes were exchanged.
∴ 66 = nC2
∴ 66 = `("n"!)/(2!("n" - 2)!)`
∴ 66 × 2 = `("n"("n" - 1)("n" - 2)!)/(("n" - 2)!)`
∴ 132 = n(n – 1)
∴ n(n – 1) = 12 × 11
Comparing on both sides, we get
n = 12
∴ 12 participants were present at the meeting.
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