# 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. - Mathematics and Statistics

Sum

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.
Then, the number of ways of selecting any 2 persons from them = nC2
Now, in all 66 handshakes were exchanged.
nC2  = 66

∴ ("n"!)/(("n" - 2)!2!) = 66

∴ ("n" xx ("n" - 1) xx ("n" - 2)!)/(("n" - 2)!) = 66 × 2

∴ n(n – 1) = 132
∴ n(n – 1) = 12 × 11
Comparing on both sides, we get
∴ n = 12
∴ The number of participants in the meeting = 12

Concept: Properties of Combinations
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Chapter 6: Permutations and Combinations - Exercise 6.6 [Page 89]

#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.6 | Q 9 | Page 89
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