We can’t just write down any prime number; we need to make sure that when you subtract one prime number from the others that you get a prime number. Since every prime number except for ‘2’ is odd, when you subtract a prime number by a prime number you will end up with an even number. Since ‘2’ is the only even number, which two primes, less than 20, result in two when you subtract one from the other?
19 and 17
13 and 11
7 and 5
5 and 3
The other prime numbers will result when we subtract 2 from a prime number. Note, how this will be the same as the greater of the prime numbers in each pair above:
19 and 2
13 and 2
7 and 2
5 and 2
That gives us a total of 8 cases. For each case, however, there are two cases, since the question is asking for absolute difference. In other words, 11 and 13 = -2, the absolute difference is 2. This gives us a total of 16 cases.
The new step is to find the total number of possible outcomes:
(21)(20) = 420.
Don’t forget to count ‘0’!
That gives us 16/420, which is 4/105, Answer (C).