Number the particles. Then let particle 1 be in bottle n, then the probability

that all three are in the one bottel is (1/10)x(1/10) that is the probability

that the other two which are equally likley to be in any bottle are both also in bottel n.

Thus the probability that they are all in the same bottle is 0.01, which is the

probability that x=1.

The probability that 2 is in bottle n and that 3 is not is (1/10)x(9/10) as

is the probability that 3 is in bottle n and 2 is not, so the probability that

there are two particles in one bottle and one in another is 18/100.

Thus the probability that they are two in one bottle and one in another is

0.18, which is the probability that x=2.

The probability that p(x=3)=1-p(x=1)-p(x=2).

RonL