If four marbles are picked at random, what is the probability

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An urn contains 6 red, 4 blue, 2 green and 3 yellow marbles.

If four marbles are picked at random, what is the probability that one is green, two are blue and one is red ?

1. 24/455
2. 13/35
3. 11/15
4. 7/91

Correct Option: A

Ways of selection of 4 marbles = n(S) = ¹⁵C_{4
Ways of selection of one green marbles = n(E₁) = ²C₁
Ways of selection of two blue marbles = n(E₂)=⁴C₂
Ways of selection of one red marble = n(E₃) = ⁶C₁
∴ Required probability = (²C₁ x ⁴C₂ x ⁶C₁) / (¹⁵C₄) = 24/455}