In the 2010 census, the population of state A in thousands was 4,784, State B was 2,984, and State C was 4,518. Apportion 16 representative seats to these three states. Assign the seats using the Hamilton apportionment method. The representation includes members from State $A$.

Step 1 ：First, calculate the total population of the three states. This is done by adding the populations of state A, state B, and state C together. In this case, the total population is \(4784 + 2984 + 4518 = 12286\) thousand.

Step 2 ：Next, calculate the standard divisor. The standard divisor is the total population divided by the total number of seats. In this case, the standard divisor is \(\frac{12286}{16} = 767.875\).

Step 3 ：Then, calculate the standard quota for each state. The standard quota is the population of the state divided by the standard divisor. For state A, the standard quota is \(\frac{4784}{767.875} = 6.23\). For state B, the standard quota is \(\frac{2984}{767.875} = 3.89\). For state C, the standard quota is \(\frac{4518}{767.875} = 5.88\).

Step 4 ：Next, assign each state the integer part of its standard quota. State A gets 6 seats, state B gets 3 seats, and state C gets 5 seats. This totals to 14 seats, leaving 2 seats unassigned.

Step 5 ：Finally, assign the remaining seats to the states with the largest fractional parts of their standard quotas. In this case, state A and state C each get one of the remaining seats. Therefore, state A gets 7 seats, state B gets 3 seats, and state C gets 6 seats.

Step 6 ：Check the solution. The total number of seats assigned is 16, which is the total number of seats available. Therefore, the solution is correct.

Step 7 ：The final apportionment of seats is: state A gets 7 seats, state B gets 3 seats, and state C gets 6 seats. This is the simplest form of the solution.