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Study the given information carefully and answer the question that follow:
A basket contains 4 red, 5 blue and 3 green marbles
If three marbles are picked at random what is the probability that either all are green or all are red ?
The total number of ways of picking three marbles from the given 12 marbles is $$^{12}C_3 = 220$$
The number of ways of picking three green marbles is $$^3C_3 = 1$$
The number of ways of picking three red marbles is $$^4C_3 = 4$$
Hence, the total number of favorable cases is $$4+1 = 5$$
Hence, the required probability is $$\frac{5}{220} = \frac{1}{44}$$
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