DK-GEORGMOHR 2021 Problem 2

Georg has a $4$ -sided die with the numbers $2, 3, 4$ and $5$ . He rolls the die $17$ times and records the result of each roll on a board, so that eventually $17$ numbers are written on it. Georg notices that the average of the $17$ numbers is an integer. Is it possible that each of the numbers $2, 3, 4$ and $5$ appears at least three times on Georg's board?