The permutation and combination are composed of numbers 1.2.3.4.5. How many of the three digits without repetition can be divided by 9

The permutation and combination are composed of numbers 1.2.3.4.5. How many of the three digits without repetition can be divided by 9

The total number is 12. The sum of the numbers in each bit of the three digit number can be divided by 9. So there are only two groups: 1, 3, 5 and 2, 3, 4

How many six digit numbers can be divided by 25 with 0,1,2,3,4,5?

Can be divided by 25, mantissa is 25 or 50
In the case of 25, 0 is not in the first place and there are 3 kinds; in the other cases, there are no restrictions and a (3,3) = 6 kinds
In the case of 50, there is no limit for the rest, a (4,4) = 24
Total: 3 × 6 + 24 = 42

Can we use 1, 2, 3, 4, 5 and 6 numbers to form a six digit number that has no repetition and can be divisible by 11? Why?

No, because the number divisible by 11 has the following characteristics: if the odd and even bit difference of a number is a multiple of 11 (or 0), then the number can be divisible by 11, otherwise it can't. That is, add the number on odd bit and the number on even bit from right to left, and then calculate their difference