Hang on, let me try

Sure no rush

Divisible by 5 means the number is a multiple of 5 or 10. So the number ends with a 0 or 5.


So last digit has to be 0 or 5.

Cases to consider :


① 3 digits, first digit is 9, last digit is 0 or 5.

Number of ways for last digit

= 2 (either 0 or 5)


Number of ways for middle digit
= 8 ( we cannot use 0 if we used 0 already for the middle digit, same for 5)




Total for case ①
= 2 x 8
= 16



② 4 digits, last digit is 5.

Number of ways first digit = 6
(We cannot have 0,5,8,or 9)

Number of ways for 2nd digit
= 8
(We cannot have 5 and already used 1 digit)

Number of ways for 3rd digit
= 7
(We cannot have 5 and already used 2 digit)

Total ways here for ②
= 6 x 8 x 7
= 336



③ 4 digits, last digit is 0.

Number of ways for first digit

= 7 (we cannot have 0, 8 or 9)

Number of ways for 2nd digit
= 8 (cannot have 0 and already used 1 digit)

Number of ways for 3rd digit

= 7 (cannot have 0 and used 2 digits alr)


Total ways for ③
= 7 x 8 x 7
= 392


Total = 16 + 336 + 392
= 744

@J sowwie your text got cut off halfway. I understood the 3 digits but I need help with 4 digits

The 4 digit one goes as follows

CASE 1: 5 as the starting digit

- Last digit must be 0, since number is divisible by 5

This leaves us with a choice of 8 digits for the hundreds place, and in each of these, 7 digits for the tens place.

Total number of ways for 5xxx
= 1 x 1 x 8 x 7
= 56

CASE 2: Other 4 digit numbers not starting in 5, 8, 9

- Last digit can be 5 or 0
- First digit can be 1, 2, 3, 4, 6, 7
- Hundreds place can be any of the remaining 8 digits
- Tens place can be any of the remaining 7 digits

Number of ways in this case
= 2 x 6 x 8 x 7
= 672

Add the two cases plus the 16 integers which are 3 digits long to get 744 integers.

We use the process of digit elimination to do such cases, in the order of ones place, thousands place, hundreds place and tens place.

I've just edited it. Are you able to see the full text now?

Yeap I can see it alr@ J thanku!

Thanku @Eric too!

You're welcome ! Our approaches are slightly different but lead to the same answer

Yeap but it’s good to learn diff methods :)

Yup indeed. The more the merrier.