<span>25/28 is the probability of picking two or three white balls.
Given that there are only 8 balls in total and of those 8, 5 of them are blue, this problem can be turned around to "What's the probability of selecting 5 blue balls?" And then subtracting that result from 1.
There are a total of 6 ways of selecting all 5 blue balls. The only difference is when the single white ball is selected. The 6 ways are BBBBBW, BBBBWB, ..., WBBBBB. So let's calculate the probability of each of those 6.
5/8 * 4/7 * 3/6 * 2/5 * 1/4 * 3/3 +
5/8 * 4/7 * 3/6 * 2/5 * 3/4 * 1/3 +
5/8 * 4/7 * 3/6 * 3/5 * 2/4 * 1/3 +
5/8 * 4/7 * 3/6 * 3/5 * 2/4 * 1/3 +
5/8 * 3/7 * 4/6 * 3/5 * 2/4 * 1/3 +
3/8 * 5/7 * 4/6 * 3/5 * 2/4 * 1/3 = ?
If you look closely at each of the 6 lines, you'll realize that the numerator will always be the product of 5!3 and the denominator will be 3*4*5*6*7*8. So, let's simplify to
6*5!3/(3*4*5*6*7*8)
= 6*5*4*3*2*3/(3*4*5*6*7*8)
= 2*3/(7*8)
= 3/(7*4)
= 3/28
Now we just need to calculate 1 - 3/28 = 28/28 - 3/28 = 25/28</span>
