An urn contains 6 red, 4 blue, 2 green 3 yellow marbles. If two marbles are drawn at random from the run, what is the probability that both are red ?

Answer: Option B

Total number of balls = (6 + 4 + 2 + 3) = 15
Let E be the event of drawing 2 red balls.
Then, n(E)  $$={}^6{C}_2$$  $$=\frac{6\times 5}{2\times 1}$$   = 15
Also, $$n(S)={}^{15}{C}_2$$   $$=\frac{15\times 14}{2\times 1}$$   = 105
$$\therefore P(E)=\frac{n(E)}{n(S)}=\frac{15}{105}=\frac{1}{7}$$