Question 1189299: James wishes to plant 27 flowers in a flower-bed.
He can choose from 17 different geraniums, 9
different roses and 7 different lilies. He wants to
have at least 13 geraniums and also to have the
same number of roses and lilies. Find the number
of different selections of flowers he can make
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
27 plants total, with the number of geraniums at least 13 and at most 17, and equal numbers of roses and lilies, the choices are
13 geraniums, 7 roses, 7 lilies
15 geraniums, 6 roses, 6 lilies
17 geraniums, 5 roses, 5 lilies
With one possible interpretation of the phrase "number of different selections of flowers", the answer is then "3".
But that is probably not the intended meaning. Presumably the desired answer is
C(17,13)*C(9,7)*C(7,7) + C(17,15)*C(9,6)*C(7,6) + C(17,17)*C(9,5)*C(7,5)
You can do the calculations....
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