Introduction:
In quantum statistics, two identical particles that are indistinguishable can be described by either Bose-Einstein statistics or Fermi-Dirac statistics. Bose-Einstein statistics apply to particles known as bosons, which can occupy the same quantum state simultaneously, while Fermi-Dirac statistics apply to particles known as fermions, which cannot occupy the same quantum state simultaneously.

Given:
We are given a system of 2 identical particles, each of which can be in any one of the 3 single particle states. We need to determine the number of states possible in Bose-Einstein statistics for this system.

Solution:
To solve this problem, we can consider the possible combinations of states that the two particles can occupy. Since the particles are identical, the order of the states does not matter.

Combination 1: Both particles in the same state
There are 3 possible states that both particles can occupy. (State 1, State 1), (State 2, State 2), (State 3, State 3)

Combination 2: One particle in State 1 and the other in State 2
There are 3 possible ways to choose the particle in State 1 and 3 possible ways to choose the particle in State 2. So, there are a total of 3 x 3 = 9 possible states for this combination.

Combination 3: One particle in State 1 and the other in State 3
Similar to Combination 2, there are 3 x 3 = 9 possible states for this combination.

Combination 4: One particle in State 2 and the other in State 3
Again, there are 3 x 3 = 9 possible states for this combination.

Total number of states:
To find the total number of states, we add up the number of states for each combination.
Total number of states = Combination 1 + Combination 2 + Combination 3 + Combination 4
Total number of states = 3 + 9 + 9 + 9 = 30

However, we need to consider that identical particles are subject to Bose-Einstein statistics, which means that the order of the particles does not matter. In other words, the states (State 1, State 2) and (State 2, State 1) are considered the same state.

Accounting for indistinguishability:
To account for the indistinguishability of the particles, we need to divide the total number of states by the number of ways the particles can be rearranged. Since there are 2 identical particles, there are 2! = 2 ways to rearrange them.

Number of states in Bose-Einstein statistics = Total number of states / Number of ways to rearrange the particles
Number of states in Bose-Einstein statistics = 30 / 2 = 15

Therefore, the correct answer is 15 states.

Correction:
Apologies for the earlier incorrect response. The correct number of states in the given system, considering Bose-Einstein statistics, is 15, not 6.