Consider a group of 20 people. If everyone shakes hands with everyone else, how many handshakes take place?
Show Hint
- \( ^{19}C_2 \)
- \( ^{20}C_2 \)
- \( ^{20}C_{19} \)
- \( 20^2 \)
The Correct Option is B
Solution and Explanation
Total number of handshakes is given by: \[ \binom{20}{2} = \frac{20 \times 19}{2} = 190 \] Conclusion: The total number of handshakes is 190.
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