Permutations and combinations - Quantitative Aptitude (MCQ) questions for Q. 21474

Q.  A box contains 4 black, 3 red and 6 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color?
- Published on 04 May 16

a. 12/74
b. 24/78
c. 13/78
d. None of these

ANSWER: 24/78
 
Total marbles in a box = 4 black + 3 red + 6 green marbles = 13 marbles
2 marbles are drawn from 13 marbles at random. Therefore,
n(S) = 13C2 = 78 ways
Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is
n(A) = 4C2 + 3C2 + 6C2 = 6 +3 + 15 = 24
Therefore, by definition of probability of event A,
P(A) = n(A)/n(S) = 24/78

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    Discussion

  • Buddhika   -Posted on 15 Aug 16
    3C2 = 78 ways- could understand the maths here. how 78 comes.

    4C2 + 3C2 + 6C2 = 6 +3 + 15 = 24- here also difficult to undestand the maths concept.
    please e mail me the explanation

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