Answer to Question #225981 in Statistics and Probability for Mustafa Zaidi

Question

A drawer contains 5 pairs of green socks, 3 pairs of black socks, and 4 pairs of red socks. The 12 pairs of socks are jumbled together in one drawer, but each sock is still attached to its mate. You reach into the drawer and pull out 3 pairs of socks, one at a time, without putting any back. What is the probability that you get 2 pairs of green socks? Leave your answer as a fraction in lowest terms. Provide evidence of your work by typing out your full solution.

ASP

Answer 1

$$P(2green\ \&\ 1other)=\dfrac{\dbinom{5}{2}\dbinom{7}{1}}{\dbinom{12}{3}}$$ $$=\dfrac{\dfrac{5!}{2!(5-2)!}\cdot\dfrac{7!}{1!(7-1)!}}{\dfrac{12!}{3!(12-3)!}}=\dfrac{10\cdot7}{220}=\dfrac{7}{22}$$

The probability that you get 2 pairs of green socks is $\dfrac{7}{22} .$