In a team every player shakes his hand with other player only once. If total number of handshakes is 120, then the number of players is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 16
Each handshake is one pair of players, and every pair shakes hands once, so the number of handshakes among \(n\) players is the number of ways of choosing 2 of them: \({}^{n}C_{2}=\frac{n(n-1)}{2}\).
\(\displaystyle\frac{n(n-1)}{2}=120\), so \(n(n-1)=240\)
240 is the product of the consecutive numbers 16 and 15, so \(n=16\)