Given that there are 10 balls in the bucket, you know that these are numbered from 1 through 10.
You can determine that the probability of drawing a ball numbered 8 is:

Since there is no replacement, the probability of drawing a ball numbered 5 in the second selection is:

Therefore:

Hence, the probability of drawing four balls numbered 8, 5, 10, and 7 without replacement is;


Therefore, the answer is:
