Answer : Option B

Explanation :

Total number of balls = 2 + 3 + 2 = 7
Let S be the sample space.
n(S) = Total number of ways of drawing 2 balls out of 7 = ⁷C₂
Let E = Event of drawing 2 balls , none of them is blue.
n(E) = Number of ways of drawing 2 balls , none of them is blue
= Number of ways of drawing 2 balls from the total 5 (=7-2) balls = ⁵C₂
(∵ There are two blue balls in the total 7 balls. Total number of non-blue balls = 7 - 2 = 5)

$MF#%\text{P(E) = }\dfrac{\text{n(E)}}{\text{n(S)}}= \dfrac{5_{C_2}}{7_{C_2}}
= \dfrac{\left(\dfrac{5 \times 4 }{2 \times 1} \right )}{\left(\dfrac{7 \times 6 }{2 \times 1} \right )}= \dfrac{5 \times 4}{7 \times 6} = \dfrac{10}{21}$MF#%