Symbiosis National Aptitude Test SNAP 2015 Paper

Total number of balls = (2 + 3 + 2) = 7
Let S be the sample space. Then,
n (S) = Number of ways of drawing 2 balls out of 7
= $\stackrel{7}{}{\mathit{C}}_2$ = $\frac{\left(7\times 6\right)}{\left(2\times 1\right)}$ = 21
Let E = Event of drawing 2 balls, none of which is blue.
∴ n (E) = Number of ways of drawing 2 balls out of (2 + 3) balls
= $\stackrel{5}{}{\mathit{C}}_2$ = $\frac{\left(5\times 4\right)}{\left(2\times 1\right)}$ = 10
∴ P (E) = $\frac{\mathit{n}\left(\mathit{E}\right)}{\mathit{n}\left(\mathit{S}\right)}$ = $\frac{10}{21}$