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Example: A garden has 4 types of flowers: roses, lilies, tulips and sunflowers. Flowers of the same type are considered identical. In how many ways can we make a bouquet of 10 flowers, if we must have at least 2 roses and 1 tulip?

my answer: $$C(n+r-1,r)=C(4+7-1,7)=\frac{10!}{7!(10-7)!}=120$$ is it correct??

Bram28
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HWK
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    Assuming that order of flowers within the bouquet doesn't matter and there is no limit to the number of each flower type available, yes it looks fine. – JMoravitz Jan 10 '20 at 18:33
  • yes, there are no limits on the numbers of each type of the flowers. – HWK Jan 10 '20 at 19:05

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Yes your answer is correct. The answer also represents the number of solutions to the following equation- $$r+l+t+s=7$$ where r, l, t, s is the number of roses,lilies, tulips and sunflowers respectively.

Sam
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