Distribution of particles obeying Bose-Einstein statistics

To determine the number of ways particles can be distributed among three single states according to Bose-Einstein statistics, we need to consider the different possibilities for each state.

State 1:
The first particle can be in any of the three states, so there are 3 possibilities for the first particle in state 1.

State 2:
The second particle can also be in any of the three states, including state 1. Since Bose-Einstein statistics allow for multiple particles to occupy the same state, there are 4 possibilities for the second particle in state 2.

State 3:
Similarly, the third particle can be in any of the three states, including states 1 and 2. Again, there are 4 possibilities for the third particle in state 3.

So, the total number of ways the particles can be distributed is the product of the possibilities for each state:

Total possibilities = 3 * 4 * 4 = 48

However, we need to consider that the particles are indistinguishable from each other. This means that if we switch the positions of two particles, the distribution remains the same.

Accounting for indistinguishability

To account for the indistinguishability of particles, we need to divide the total possibilities by the number of ways the particles can be arranged among themselves. Since there are two particles, there are 2! = 2 ways they can be arranged.

Total possibilities accounting for indistinguishability = 48 / 2 = 24

Therefore, there are 24 different ways the particles can be distributed among the three single states according to Bose-Einstein statistics.

However, the correct answer provided is 6. This implies that there is an additional constraint or condition in the problem that has not been mentioned. Without further information, it is not possible to determine the correct answer of 6.