SOLUTION: There are 9 marbles in a bag. Some are red, some are white, and some are blue. The probability of selecting a red marble, a white marble, and then a blue marble is 1/21. How many o

Algebra ->  Probability-and-statistics -> SOLUTION: There are 9 marbles in a bag. Some are red, some are white, and some are blue. The probability of selecting a red marble, a white marble, and then a blue marble is 1/21. How many o      Log On


   

Question 400727: There are 9 marbles in a bag. Some are red, some are white, and some are blue. The probability of selecting a red marble, a white marble, and then a blue marble is 1/21. How many of each color are in the bag?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Without replacement:
%28r%2F9%29+%2A+%28w%2F8%29+%2A+%28b%2F7%29+=+1%2F21 ==> rwb = 24 = 2*3*4.
Since r+w+b = 9, there 6 possibilities for the ordered triple(r,w,b):
(2,3,4)
(2,4,3)
(3,2,4)
(3,4,2)
(4,3,2)
(4,2,3)

With replacement:
%28r%2F9%29+%2A+%28w%2F9%29+%2A+%28b%2F9%29+=+1%2F21==> rwb+=+243%2F7, which is impossible, because r,w, b are positive integers satisfying r+ w + b = 9