How many 4-digit numbers are there that are divisible by 10 and the sum of whose digits is 10?

Question

How many 4-digit numbers are there that are divisible by 10 and the sum of whose digits is 10?

Answer 1

Well as they are divisible by 10, the last digit must be 0.

To choose the first three digits you choose 3 digits sum is 10.

First cannot be zero.

So you can have

1 09 18 27 36 45 54 63 72 81 90

2 08 17 26 35 44 53 62 71 80

3 07 16 25 34 43 52 61 70

4 06 15 24 33 42 51 60

5 05 14 23 32 14 05

6 04 13 22 31 40

7 03 12 21 03

8 02 11 02

9 01 10

So 2+3+4+5+6+7+8+9+10 possible combinations with the last digit being zero