A box contains 5 black, 10 white and 8 yellow marbles. 4 marbles are drawn from the box at random. What is the probability that all three marbles are of the same color? Choose the correct option.
A) 224/8855 B) 225/8855 C) 245/8855 D) 285/8855 E) 244/8855
Explanation:   Total marbles in a box = 5 black +10 white + 8 yellow marbles = 23 marbles   4 marbles are drawn from 23 marbles at random. Therefore,   n(S) = 23C4 = 8855 ways   Let A be the event that 4 marbles drawn at random are of the same color. Number of cases favorable to the event A is   n(A) = 5C4 + 10C4 + 8C4 = 5 +210 + 70= 
<gadget id="calculator">5 +210 + 70</gadget>
<output>285</output>
285   Therefore, by definition of probability of event A,   P(A)= n(A)/n(S) =285/8855   ANSWER:285/8855
<result>D</result>
A box contains 5 black, 10 white and 8 yellow marbles. 4 marbles are drawn from the box at random. What is the probability that all three marbles are of the same color?