KCET · Maths · Permutation Combination
Everybody in a room shakes hands with everybody else. The total number of handshakes is
45. The totalnumber of persons in the room is
- A \( 09 \)
- B \( 10 \)
- C \( 05 \)
- D \( 15 \)
Answer & Solution
Correct Answer
(B) \( 10 \)
Step-by-step Solution
Detailed explanation
Total number of handshakes are \( 45 . \)
So, total number of persons are
\[
\begin{array}{l}
{ }^{n} C_{2}=45 \\
\Rightarrow \frac{n(n-1)}{2}=45 \\
\Rightarrow n(n-1)=90 \Rightarrow 10 \times 9 \\
\Rightarrow n(n-1)=10(10-1) \\
\Rightarrow n=10
\end{array}
\]
So, total number of persons are
\[
\begin{array}{l}
{ }^{n} C_{2}=45 \\
\Rightarrow \frac{n(n-1)}{2}=45 \\
\Rightarrow n(n-1)=90 \Rightarrow 10 \times 9 \\
\Rightarrow n(n-1)=10(10-1) \\
\Rightarrow n=10
\end{array}
\]
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