Permutations Practice Test 1

Question : 16 of 40

Marks: +1, -0

Everybody in a room shakes hands with everybody else. The total number of hand shakes is 66. Thetotal number of person in the room is:

Solution:

Let there be n persons in a room.
∴ Total no. of shakehands

= ^nC_2 = 66

⇒1/2 n(n - 1) = 66

⇒ n^2 - n - 132 = 0

⇒ (n + 11) (n -12) = 0

∴ n = 12

(∵n ≠ -11)

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