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

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) (Show Source): You can put this solution on YOUR website!

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) =
P(BBB) =
P(YYY) =
Probability of choosing five marble of any one of the three colours
= P(GGG) + P(BBB) + P(YYY) =

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

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