There are 9 positive and 5 negative numbers. Four numbers.........What is the probability that the product is positive?

Question

There are 9 positive and 5 negative numbers.
Four numbers are chosen at random and multiplied.
What is the probability that the product is positive?

Answer 1

All Positive number case (Yields positive product) = 9C4/14C4 = 126/1001 [Probabilty P1]
All Negative case (Yields positive product) = 5C4/14C4 = 5/1001 [Probabilty P2]
2 Positive and 2 Negative case (Yields positive product) = 9C2*5C2/14C4 = 36*10/1001 = 360/1001[Probabilty P3]
Required Probabilty P = P1 + P2 + P3 = (126 + 5 + 360)/1001 = 491/1001 = 0.4905 = 49.05%.