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 500,000 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:
Halle, Julia and Drew have 5 donuts to share. If one of them [#permalink]
13 Oct 2004, 21:04
5
This post was BOOKMARKED
00:00
A
B
C
D
E
Difficulty:
(N/A)
Question Stats:
50% (01:23) correct
50% (04:21) wrong based on 27 sessions
Halle, Julia and Drew have 5 donuts to share. If one of them can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed.
Re: Halle, Julia and Drew have 5 donuts to share. If one of them [#permalink]
16 Oct 2004, 06:51
1
This post received KUDOS
1
This post was BOOKMARKED
Hmmm.
This is a combinations with repetition problem.
Just have to think about it the right way. Basically we have a bag of donuts from which we will pull 5 times. Any donut removed from the bag can be a Halle, Julia, or Drew Donut.
The general formula is:
C(n+r-1,r)
n number of elements
r-combinations.
So
C(5+3-1,5) = C(7,5) = C(7,2) = 21
The way that this makes sense is if we consider aligning the 5 donuts (*) and placing separators between them to indicate to whom they belong.
So,
*****||
would indicate that Halle has all the donuts,
|*****|
would indicate that Julia has all the donuts, and
||*****
would indicate that Drew has all the donuts.
So the answer is the number of ways to pick the 5 *'s or the 2 |'s out of the set of 7.
Re: Halle, Julia and Drew have 5 donuts to share. If one of them [#permalink]
16 Oct 2004, 23:02
1
This post received KUDOS
2
This post was BOOKMARKED
tygel, this is a great logic
Extending this logic further can also be used to solve problems like these:
1. In how many ways can 20 be expressed as sum of 5 non negative integers.
using similar logic : you have 20 *s are 4 seperators '|' and u have to chose 4 '|' and u can do that in 24C4 ways.
TO add to this twist, in how many ways can the number 20 be written as a sum of 5 positive integers? you have 20 *'s and u have to place 4 '|' in between them, i.e. no of ways in which 4 '|' can be placed in 19 places, where all '|' are identical. 19C4.
To summarise, no of ways in which n things can be divided among r persons so that each of them can receive 0 or more is n+r-1Cr-1. In tapsemi's Q. n= 5, r = 3, so reqd ways = 7C2 = 21.
and no of ways in which n things can be divided among r persons so that each of them receive at least 1 is n-1Cr-1
Re: Halle, Julia and Drew have 5 donuts to share. If one of them [#permalink]
08 Aug 2015, 12:40
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________
Re: Halle, Julia and Drew have 5 donuts to share. If one of them [#permalink]
24 Oct 2015, 08:30
tapsemi wrote:
Halle, Julia and Drew have 5 donuts to share. If one of them can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed.
As I’m halfway through my second year now, graduation is now rapidly approaching. I’ve neglected this blog in the last year, mainly because I felt I didn’...
Hilary Term has only started and we can feel the heat already. The two weeks have been packed with activities and submissions, giving a peek into what will follow...
Ninety-five percent of the Full-Time Class of 2015 received an offer by three months post-graduation, as reported today by Kellogg’s Career Management Center(CMC). Kellogg also saw an increase...