A basket contains 4 red, 5 blue and 3 green marbles. If 2 marbles are drawn at random from the basket, What is the probability that both are red ?

Answer: Option C

Total number of balls = (4 + 5 + 3) = 12
Let E be the event of drawing 2 red balls.
Then, n (E) = $${}^4{C}_2=\frac{4\times 3}{2\times 1}$$   = 6
Also n (S) = $${}^{12}{C}_2=\frac{12\times 11}{2\times 1}$$   = 66
$$\therefore P(E)=\frac{n(E)}{n(S)}=\frac{6}{66}=\frac{1}{11}$$