Mathematics, looking for probability

First consider the situation of each dice:

Each dice will wait for six possible situations (1 to 6 o'clock * * *), so the probability of the four points you bought (1234) is 4/6=2/3, and the probability of not appearing is 1/3.

A * * * has three dice,

The winning prize is that each dice appears with a 2/3 probability of 1234, and the probability is (2/3) 3 = 8/27, but three identical numbers are not allowed. Subtract the four probabilities of three 1, 2, 3 and 4 * *, that is, 4 * (1/6).

That is, the winning probability is 8/27- 1/54=5/ 18.

Two of the three dice appear 1234 with a probability of 2/3. These two dice have three arrangements (12, 13,23), and the remaining 1 dice appear with a probability of13.

The probability is 3 * (2/3) 2 * (1/3) = 4/9.