An urn contains 2 yellow, 4 green, 1 white and 3 red marbles. If two marbles are drawn at random from the urn, then what is the probability that both are green ?

$\frac{2}{15}$

Total number of marbles in urn = 10

Number of selecting 2 marbles = \(\frac{10 × 9 × 8! }{8! × 2 × 1  }\) = 45

number of green marbles = 4

Number of selecting 2 green marbles = \(\frac{4 × 3 × 2! }{2! × 2 × 1  }\) = 6

Probability that both drawn marbles are green = \(\frac{ 4C2 }{ ¹⁰C2 }\)

= \(\frac{ 6 }{ 45 }\)

= \(\frac{ 2 }{ 15 }\)

The correct answer is option (2) : $\frac{2}{15}$