There are two red, two blue, two white, and certain number (greater than `0`) of green socks in a drawer. If two socks are taken at random from the drawer `4` without replacement, the probability that they are of the same color is `1/5`, then the number of green socks are ________.

Answer

D

Explanation

Let the number of green socks be `x gt 0`.
E: Two socks drawn are of the same color
implies P(E) = P(R R or B B or W W or G G)
`=(3)/(.^(6+x)C_(2)) + (.^(x)C_(2))/(.^(6+x)C_(2))`
`=(6)/((x + 6)(x + 5))+(x (x-1))/((x+6)(x+5)) = (1)/(5)`(given)
`implies 5(x^(2) - x + 6) = x^(2) + 11x + 30`
`or 4x^(2) - 16x = 0`
or x = 4