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

  • $\begingroup$ 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

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.

  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.