Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

John has 7 bananas and 3 kiwis. In how many ways can John [#permalink]
01 Feb 2005, 18:23

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct
0% (00:00) wrong based on 0 sessions

John has 7 bananas and 3 kiwis. In how many ways can John divide the 10 fruit between 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.

1. 1 k + 4 b or 2 k + 3 b
3C1 * 7C4 = 3 x 35 = 105 possibilities
2. 2 k + 3 b or 1 k + 4 b
3C2 * 7C3 = 3 x 35 = 105 possibilities
3. parcel 1 is equal to parcel 2 => only 105 possibilities at all

We need to select 5 from 10, with at least 1 kiwi.

1 kiwi C(3,1)C(7,4)=3*7*6*5/6=105

And that's it. No need to do two kiwis since it is symmetric.

Can you explain a little more?

According to your result, it only answers this question:

In how many ways can John divide the 10 fruit between two parcels, if there has to be an equal total number of fruit in either parcel and so that there is only one kiwi in one parcel and two in the other.

It's the same. One in this bag means two in the other bag. And two in this bag means one in the other bag. Say you only have three fruits. I treat the following two case as the same outcome:
A has f1 and B has f2, f3
A has f2, f3 and B has f1

We need to select 5 from 10, with at least 1 kiwi.

1 kiwi C(3,1)C(7,4)=3*7*6*5/6=105

And that's it. No need to do two kiwis since it is symmetric.

Here's what I don't get. I see two possiblities:
A. 4 bananas and 1 kiwi (7c4 * 3c1) 105 possibilities
B. 3 bananas and 2 kiwi (7c3 * 3c2) 105 possibilities

total # of poss = 210

what am I missing? I understand that the two parcels are symmetric, but you still have different fruits in case one vs. case two.

box1- 7C3 AND 3C2 OR 7C4 AND 3C1 = 105 + 105 = 210 box2- 7C4 AND 3C1 OR 7C3 AND 3C2 = 105 + 105 = 210

TOTAL=210+210 = 420 possibilities.

now where am i going wrong??????????? can anybody tell me plz

parcel 1: kbbbb (case1) OR kkbbb(case2) = 105 p (you misused OR as AND)
parcel 2 : kkbbb(case1) OR kbbbb(case2) = 105 p (you misused OR as AND)

it is a combination problem that means it does not matter which parcel has the combination; it only matters the different way of combinations; in your approach you count the combination that appears in parcel 1 as well as the combination in parcel 2, but you should count it only once. maybe it helps

box1- 7C3 AND 3C2 OR 7C4 AND 3C1 = 105 + 105 = 210 box2- 7C4 AND 3C1 OR 7C3 AND 3C2 = 105 + 105 = 210

TOTAL=210+210 = 420 possibilities.

now where am i going wrong??????????? can anybody tell me plz

parcel 1: kbbbb (case1) OR kkbbb(case2) = 105 p (you misused OR as AND) parcel 2 : kkbbb(case1) OR kbbbb(case2) = 105 p (you misused OR as AND)

it is a combination problem that means it does not matter which parcel has the combination; it only matters the different way of combinations; in your approach you count the combination that appears in parcel 1 as well as the combination in parcel 2, but you should count it only once. maybe it helps

ways to pick 5 fruits from 10 - ways to pick 5 friuts with all 3 kiwis - ways to pick 5 fruits with no kiwis
=10C5-8C3-7C5
=175

Note in both parcels there should be atleast 1 kiwi.Meaning you can not have 3 kiwis picked in the first parcel(second parcel will have zero kiwis), andyou can not have no kiwis at all.

I´ve done an interview at Accepted.com quite a while ago and if any of you are interested, here is the link . I´m through my preparation of my second...

It has been a good week so far. After the disappointment with my GMAT score, I have started to study again, re-schedule the new test date and talked with...

It’s here. Internship season. The key is on searching and applying for the jobs that you feel confident working on, not doing something out of pressure. Rotman has...