Lets award Calvin ,Satvik and Utsav!

Well, this is a nice easy problem!

Suppose that one person gets 4 prizes(the maximum one can get).

Then, he can have $\left( \begin{matrix} 6 \\ 4 \end{matrix} \right)$ combinations of prizes. Also, the other 2 can have $\left( \begin{matrix} 2 \\ 1 \end{matrix} \right)$ combinations of prizes for each combination, which means there are $\left( \begin{matrix} 6 \\ 4 \end{matrix} \right) \left( \begin{matrix} 2 \\ 1 \end{matrix} \right)$ combinations for 4 prizes for one guy. But there are three so, in total $3 \left( \begin{matrix} 6 \\ 4 \end{matrix} \right) \left( \begin{matrix} 2 \\ 1 \end{matrix} \right)$ combinations.

Similarly, we can find for 3 for one guy and 2 for one guy too such that when we add all of them, we get this-

$3\left[ \left( \begin{matrix} 6 \\ 4 \end{matrix} \right) \left( \begin{matrix} 2 \\ 1 \end{matrix} \right) \quad +\quad \left( \begin{matrix} 6 \\ 3 \end{matrix} \right) \left( \begin{matrix} 3 \\ 2 \end{matrix} \right) 2\quad +\quad \left( \begin{matrix} 6 \\ 2 \end{matrix} \right) 2 \right] \quad$ which is simply $\boxed{540}$