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.

Answer 1

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.