Here is another way.
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Probability is favorable to possible.
What is favorable?
{1,2,3} All premutations of this set = 6
{2,3,4} All premutations of this set = 6
.....
{18,19,20} All premutations of this set = 6
In total we have,
18 Sets
Thus,
The possible outcomes is the number of ways of selecting 3 out of twenty.
Which is,
Thus,