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Two girls have picked 10 roses, 15 sunflowers and 15 daffodils. What is the number of ways they can divide the flowers amongst themselves ?

(a) 1638
(b) 2100
(c) 2640
(d) None of the above

My approach:

By applying Stars and Bars where bins can be empty, I'm getting =$\binom{10+2-1}{1}\times\binom{15+2-1}{1}\times\binom{15+2-1}{1}=2816$

Which is not in the option, what I have assumed wrong

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  • $\begingroup$ Any restrictions on what sort of flowers each girls can have? $\endgroup$ – Alex Feb 5 '15 at 22:22
  • $\begingroup$ What about option $d)$ ? $\endgroup$ – Peter Feb 5 '15 at 22:35
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The number of roses, girl $1$ gets, has $11$ possibilities, for the other flowers we have $16$ possibilities. So, there are $11\times 16\times 16=2816$ ways to divide the flowers.

So, option $d)$ is correct.

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  • $\begingroup$ The girls are distinct. Your solution does not count cases where girl 1 does not have any flowers of a particular kind. Answer would be 11*16*16 $\endgroup$ – Angad Feb 5 '15 at 23:29
  • $\begingroup$ Oops, you are right. I edited my answer. $\endgroup$ – Peter Feb 5 '15 at 23:31

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