combination related question suppose that  dinner cooker  has  500 mint,500 orange and  500 strawberry,and he wished to do packets  containing 10 mint,5 orange and 5 strawberry,question is  what is a maximum number of packets  he can make  by this  way?
so as i think,it is a  combination related problem,which means that  we can choose  how many   10 mint we can choose from 500 mint or
$500!/(10!*490!)+500!/(5!*495!)+500!/(5!*495!)$,but no calculator can calculate  factorial of $500$ and how can i solve it more easily?

After making 50 packets, you've used up $500=50\times 10$ mint, $250=50\times 5$ orange, and $250=50\times 5$ strawberry.  There is no mint left, so you can't make any more.
