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John has 7 bananas and 3 kiwis. In how many ways can John

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Director
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John has 7 bananas and 3 kiwis. In how many ways can John [#permalink] New post 06 Feb 2007, 09:17
John has 7 bananas and 3 kiwis. In how many ways can John divide the 10 fruit b/w two parcels, if there has to be an equal total number of fruit in either parcel and so that there is at least one kiwi in each parcel?

If you can, please try and use the:

total outcome - unfavorable outcome(s) approach
Senior Manager
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 [#permalink] New post 06 Feb 2007, 09:54
if all bananas are similar and all kiwis are similar ..then there is only 2 ways.

if fruits are distinct then

one of the parcel contain 1 kiwi and 4 bananas and remaining fruits will be in second parcel

3C1 * 7C4 = 105
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 [#permalink] New post 06 Feb 2007, 12:57
in fact.... if the parcels are also not distinct, there is only one option:
one parcel with 2 kiwis (+ 3 banans) and the other 1 kiwi (+4 bananas)...

another comment:
Quote:
If you can, please try and use the:

total outcome - unfavorable outcome(s) approach


it is not good, in my opinion, to try "forcing" the use of a method to a certain question. it is usually a sign that you try to master, or understand one methodology, and treat it as a "one method for all".

it is never the case in math. there is no "one best method" or "one fits all" technique. there is a wide range of them, and each maybe applied to a different set of questions.

in fact, i would claim, that the different methods are relatively easy to grasp and use, whats difficult is choosing the best one for a given question.

to practice that - the one thing that you don't want is to force a certain method on the given question. what you need is a diverse set of questions, and a lot of patience in analyzing the questions.

not only to understand how the method worked for this question (what most people do when reading OEs) but rather find what in the question implied or invited the use of this method. what "hidden signals" are there that can help you go the short and easy path to the answer.... looking for these signs is the true studying of the GMAT math (my opinion only....)
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 [#permalink] New post 06 Feb 2007, 14:28
Since we need to have atleast one 1 KIWI 3 KIWIs can be divided into 2 parcels in only 1 way that is

1 KIWI in 1st parcel
2 KIWIs in 2nd parcel

Now since we have to have equal # of fruits in each parcel bananas can be distributed also only in 1 way

4 BANANAs in 1st parcel
3 BANANAs in 2nd parcel

Hence, there is only one way to do this.
_________________

"Live as if you were to die tomorrow. Learn as if you were to live forever." - Mahatma Gandhi

  [#permalink] 06 Feb 2007, 14:28
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John has 7 bananas and 3 kiwis. In how many ways can John

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