Could anyone please solve this question using counting?

S = [2,3,5,7,11,13,17,19]

- P(<31)

19 will never give us < 31, because when multiplied with the smallest 2 numbers (2,3), it gives us a number > 31

Same with 17, 13, 11, 7

The only group that we have is 2, 3, 5 (group of 3)

The probability that the number is chosen from desired group is = \frac{3}{8} * \frac{2}{7} * \frac{1}{6} = \frac{1}{56}

- To get an odd number from the sum of three numbers, the numbers must either be:

3 odd numbers

or 1 odd and 2 even numbers

As we have only 1 odd number is S the second is not possible

P(ooo) = \frac{7}{8} * \frac{6}{7} * \frac{5}{6} = \frac{5}{8}

Ans is positive difference b/w the two = \frac{5}{8} - \frac{1}{56} = \frac{35 - 1}{56} = \frac{34}{56} = \frac{17}{28}