Counting and probability

Could anyone please solve this question using counting?

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

  1. 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}

  1. 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}