Therefore, 4×3×3×3 = 972 species.
2. First of all, we should know that the sum of the numbers on each bit of a multiple of 3 is a multiple of 3.
Consider the case of 0 first. Possible combinations of numbers that constitute multiples of 3 are: 0, 0, 3, 0, 2, 4, 0, 2, 7, 0, 3, 3, 0, 4, 5, 0, 5, 7.
Among them, 0,0,3 can only form 300, 0,3,3 can only have two permutations 303 and 330, and the rest can have four permutations. For example, 0, 2 and 4 can form 204, 240, 402 and 420.
So there are 0 cases of *** 1+2+4×4= 19 species.
Consider again the case where there is no 0,
First, the same three numbers must be multiples of 3, including 222, 333, 444, 555, 777 * *.
Second, there are two combinations of the same numbers: 2, 2, 5, 2, 5, 5, 4, 4, 7, 4, 7. There are three arrangements for each combination. For example, 2,2,5 can form 225,252,522. So ***3×4= 12 kinds.
3. The combination of three different numbers is: 2, 3, 4, 2, 3, 7, 3, 4, 5, 3, 5, 7. There are six arrangements for each combination. For example, 2,3,4 can form 234,243,324,342,423,432. So ***6×4=24 kinds.
To sum up, *** 19+5+ 12+24=60 species.
I hope I can help you.