Hi Sophie,

There are not that many so you can list them all. Reading from left to right there are 4 choices for the first digit, 0, 1, 2 or 5. Once you have chosen the first digit there are 3 choices for the second digit since you can't repeat the first. Thus there are $4 \times 3$ choices for the first two digits. Again, regardless of what two digits you have chosen there are 2 choices for the third digit and hence $4 \times 3 \times 2$ choices for the first three digits. Finally you have only one choice for the fourth digit so in total there are $4 \times 3 \times 2 \times 1 = 24$ possibilities.

But you want to list tem.

If the first two digits are 0 and 1 then the possibilities are

0125 and
0152.

If the first two digits are 0 and 2 then the possibilities are

0215 and
0251.

If the first two digits are 0 and 5 then the possibilities are

0512 and
0521.

Thus there are six possibilities if the first digit is 0.

What if the first digit is 1 or 2 or 5?

Penny