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:

When each player shakes hands with every other player exactly once, the total number of handshakes can be calculated using the combination formula.

For $n$ players, each player shakes hands with $(n-1)$ other players. However, this counts each handshake twice (once for each person involved), so the total is divided by 2.

Number of handshakes $= \dfrac{n(n-1)}{2}$

Given that the total number of handshakes is 120:

$\dfrac{n(n-1)}{2} = 120$

$n(n-1) = 240$

$n^2 - n = 240$

$n^2 - n - 240 = 0$

Factoring the quadratic equation, we need two numbers that multiply to $-240$ and add to $-1$.

These numbers are $16$ and $-15$.

$(n - 16)(n + 15) = 0$

$n = 16$ or $n = -15$

Since the number of players must be positive, $n = 16$.

Therefore, the number of players is 16.