Re: Probability

Hello. I was solving a problem but I got a different answer than my friend.
Could anyone tell me which answer is wrong and where is a mistake?
The problem is:
Three balls are to be randomly selected with replacement from an urn
containing 20 balls numbered 1 through 20. If we bet at least one of the
drawn balls has a number as large as 17 or larger than 17, what is the
probability that we win the bet?
I got:
P{X=3} (3 balls are >=17) = 1/5 *1/5 * 1/5 = 1/125
P{X=2} (2 balls are >=17) = 3 * 1/5 * 1/5 * 4/5 = 12/125
P{X=1} (1 ball is >=17) = 3 * 1/5 * 4/5 * 4/5 = 48/125
P{X=0} (0 balls are >=17) = 4/5 * 4/5 * 4/5 = 64/125

So the probability of winning is P{X=3} + P{X=2} + P{X=1} = 61/125

Now there is another approach:

Let X denote the largest number selected.
P{X=20} = P{X=19} = P{X=18} = P{X=17}= [20 choose 2]/[20 choose 3] = 1/6
So the probability of winning is 4/6 = 2/3
Could anyone tell me which approach is correct and why the second one is not
correct?

Tad