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Home » Everybody in a room shakes hands with everybody else. The total number of hand shakes is 66. The total number of persons in the room is A. 11 B. 12 C. 13 D. 14
Everybody in a room shakes hands with everybody else. The total number of hand shakes is 66. The total number of persons in the room is A. 11 B. 12 C. 13 D. 14
CBSE | Class 11 | Maths | NCERT Exemplar | Permutations and Combinations
Everybody in a room shakes hands with everybody else. The total number of hand shakes is 66. The total number of persons in the room is A. 11 B. 12 C. 13 D. 14

Solution:

Option (B) 12 is correct.

Explanation:

It is known that,

{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}

=\frac{n !}{r !(n-r) !}

Let total time of handshakes = {}^n{C}_2 = 66

\frac{n!}{2!(n-2)}=66

\frac{n(n-1)}{2}=66

\rightarrow {n}^{2}-n=132

\rightarrow {(n-12)(n+11)}

n=12 or n={-}11

Hence, n=12

As a result, Option (B) 12 is the correct answer.

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