$A$ special lottery is to be held to select a student who will live in the only deluxe room available in a hostel. $100$ $III$ year,$150$ $II$ year,and $200$ $I$ year students have applied for the room. Each $III$ year student's name is placed in the lottery $3$ times,each $II$ year student's name $2$ times,and each $I$ year student's name $1$ time. The probability that a $III$ year student gets the room is:

• A
  $\frac{1}{8}$
• B
  $\frac{2}{9}$
• C
  $\frac{2}{7}$
• D
  $\frac{3}{8}$