To solve the expression \((199 + 2641 \cdot 2) : 27\), we first need to perform the multiplication inside the parentheses, and then we can do the addition before dividing by 27.
Calculate \(2641 \cdot 2\): \[ 2641 \cdot 2 = 5282 \]
Add 199 to the result: \[ 199 + 5282 = 5481 \]
Now, divide the sum by 27: \[ 5481 \div 27 = 203 \]
So, the final result is: \[ \boxed{203} \]