SOLUTION: In a bag there are 7 green, 9 black and 6 yellow marbles. In how many ways can 5 marbles be randomly selected from the bag, without replacement, if the selection shows all 5 marble

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Question 946336: In a bag there are 7 green, 9 black and 6 yellow marbles. In how many ways can 5 marbles be randomly selected from the bag, without replacement, if the selection shows all 5 marbles are of the same color?
Answer by mathmate(429) About Me  (Show Source):
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Given
A bag containing 7 green, 9 black and 6 yellow marbles for a total of 22 marbles.
Five marbles are picked without replacement.
Find probability of all five are of the same colour.

Solution
Randomly picked five marbles without replacement out of 22.
There are three possible colours.
P(GGG) = 7%2F22%2A6%2F21%2A5%2F20+=+1%2F1254
P(BBB) = 9%2F22%2A8%2F21%2A7%2F20+=+1%2F209
P(YYY) = 6%2F22%2A5%2F21%2A4%2F20%2A3%2F19%2A2%2F18+=+1%2F4389
Probability of choosing five marble of any one of the three colours
= P(GGG) + P(BBB) + P(YYY) = 1%2F1254+%2B+1%2F209+%2B+1%2F4389+=+17%2F2926+=+0.58%25

Answer
The probability of randomly choosing 5 marbles of the same colour is approximately 0.58%