Roses are shipped in packages of 9 roses, each containing 3 red roses and 6 whit

Question

Roses are shipped in packages of 9 roses, each containing 3 red roses and 6 white roses. A florist asks
his color-blind assistant (who cannot tell the difference between red and white roses) to arrange two
such packages into 3 bouquets, each containing 6 roses. Since the assistant cannot distinguish red
from white, assume that all possible groupings of the 18 roses into groups of 6 are equally likely.
(a) What is the probability that the 3 bouquets produced by the assistant each contain exactly two
red roses?
(b) What is the probability that any 2 of the 3 bouquets produced by the assistant contain the
same number of red roses?

Explanation / Answer

excel formula:

1st bouquet 2nd bouquet 3rd bouquet 0.399968 0.454545 1 0.181803 total no. of combinations possible= 3 probability= 0.54541

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