Instructions: Study the given information carefully to answer the questions that follows.

An urn contains 4 green, 5 blue, 2 red and 3 yellow marbles.

Question 78

If eight marbles are drawn at random, what is the probability that there are equal numbers of marbles of each colour?


In order to have equal number of marbles in each colour one has to draw 2 marbles from each colour.
Out of four green marbles two can be choosen in 4C2 ways
Out of five green marbles two can be choosen in 5C2 ways
Out of two red marbles two can be choosen in 2C2 ways
Out of three yellow marbles 2 can be choosen in 3C2 ways
So the probability is = ( 4C2 + 5C2 + 2C2 + 3C2 )/(14C8) = $$\frac{60}{1001}$$

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