Q.There are 6 positive and 8 negative numbers. Four numbers are chosen at random, without replacement, and multiplied. Find the probability that the product is a positive number.

14 numbers total (6 positive, 8 negative), $n(S)=\binom{14}{4}=1001$. The product is positive when 0, 2, or 4 of the chosen numbers are negative: $\binom{6}{4}\binom{8}{0}+\binom{6}{2}\binom{8}{2}+\binom{6}{0}\binom{8}{4}=15(1)+15(28)+1(70)=15+420+70=505$.

Split into cases by how many of the 4 chosen numbers are negative (must be even for a positive product), and sum the combination counts for each case.

Forgetting the case of 0 negatives (all 4 positive), which also gives a positive product and must be included alongside the 2-negative and 4-negative cases.