Mitumum wrote:

The only easy way is to use permutation and combination formula,that's where the 5*4*3*2*1 come from.

But I do not how to explain this concept to kids, maybe use examples? I do not think this is in primary math curriculum.

Once they know the formula, then it is not so tricky. But if they don't, it is really hard.

I would say look at each digit in turn.

There are 5 possibilities for the first digit 0, 2, 5, 7, 9.

Then for each of these there are 4 possibilities for the second digit (because you've already used up one of the 5 for the first digit).

Then similarly for each of these there are 3 possibilities for the 3rd digit, 2 for the 4th digit and finally only one possibility for the last digit as there's only one digit left by then as you've already used up the other 4 by then.

That's where the 5 * 4 * 3 * 2 * 1 comes from.

And then as you say you need to exclude all the cases beginning 97***, 95*** and 0****, which can be worked out in the same way.

So basically its 5! - 4! - 2(3!)