To determine the total number of handshakes among ten people where each person shakes hands with every other person exactly once, we can use the formula for combinations.
The formula for the number of ways to choose 2 people from \( n \) people is given by:
\[ \binom{n}{2} = \frac{n(n-1)}{2} \]
In this case, \( n = 10 \). Plugging this into the formula, we get:
\[ \binom{10}{2} = \frac{10 \cdot 9}{2} = \frac{90}{2} = 45 \]
Thus, the total number of handshakes is \( 45 \).
Therefore, the answer is:
\[ \boxed{45} \]