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  4. Everybody in a room shakes hands with everybody else. The total number of handshakes is 45. The total number of persons in the room is

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Q. Everybody in a room shakes hands with everybody else. The total number of handshakes is 45. The total number of persons in the room is

KCETKCET 2018Permutations and Combinations

Solution:

Number of handshakes = 45
$\Rightarrow \, {^nC_2} = 45$
$ \Rightarrow \, n(n-1) = 90$
$\Rightarrow \, n = 10$