BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Number of ways of Project Allocation

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 1799
Joined: Wed Dec 24, 2008 3:03 amFollowed by: 2 members
Thanked: 36 times
by goelmohit2002 » Thu Aug 27, 2009 12:54 am
An instructor will assign seven projects to three students. If two students each got two projects each, and the other one got 3 projects. In how many ways can the instructor allocate the seven projects to three students.

[spoiler]OA = 630. Can someone please tell how ?[/spoiler]
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Legendary Member
Posts: 752
Joined: Sun May 17, 2009 11:04 pm
Location: Tokyo
Thanked: 81 times
GMAT Score:680

by tohellandback » Thu Aug 27, 2009 1:10 am
trick is when you select the 2 students who get 2 books from the three students, you are automatically selecting the 3rd student who gets the 3 books, because there are only 3 books left.
Answer is:

7C2 *5C2 * 3C2= 630
The powers of two are bloody impolite!!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 1799
Joined: Wed Dec 24, 2008 3:03 amFollowed by: 2 members
Thanked: 36 times

by goelmohit2002 » Thu Aug 27, 2009 1:33 am
tohellandback wrote:trick is when you select the 2 students who get 2 books from the three students, you are automatically selecting the 3rd student who gets the 3 books, because there are only 3 books left.
Answer is:

7C2 *5C2 * 3C2= 630
sorry I could not get your reasoning....

Based on your reasoning I guess the correct answer should have been like:

7C2 * 5C2 * 3C3

Can you please tell why are you selecting 2 from 3 books left at the end ?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 752
Joined: Sun May 17, 2009 11:04 pm
Location: Tokyo
Thanked: 81 times
GMAT Score:680

by tohellandback » Thu Aug 27, 2009 1:40 am
goelmohit2002 wrote:
tohellandback wrote:trick is when you select the 2 students who get 2 books from the three students, you are automatically selecting the 3rd student who gets the 3 books, because there are only 3 books left.
Answer is:

7C2 *5C2 * 3C2= 630
sorry I could not get your reasoning....

Based on your reasoning I guess the correct answer should have been like:

7C2 * 5C2 * 3C3

Can you please tell why are you selecting 2 from 3 books left at the end ?
its not the books I am selecting. its the 2 guys I am selecting out of three so that they can get 2 books each.
The third guy obviously gets 3 books

Ok lemm explain:

1st guy gets two books= 7C2 ways
2nd guy gets 2 books= 5C2 ways-(because 5 books left)

third guys gets the three books left, nothing to do here

now those first two guys can be selected in 3C2 ways.
we don't need to select the third guy. because when we select the two guys, we automatically select the third guy who gets the remaining 3 books..
Last edited by tohellandback on Thu Aug 27, 2009 3:50 am, edited 1 time in total.
The powers of two are bloody impolite!!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 156
Joined: Sat Jul 19, 2008 6:41 am
Thanked: 8 times

IMO 630

by enniguy » Thu Aug 27, 2009 3:25 am
<edited> 630 it is. </edited>

There are three students out of which one gets 3 books. Total number of ways to decide who gets 3 books = 3.

Now, a student can be given 3 books out of 7 books in
7C3 = 35 ways.

The next student can be given 2 books out of remaining 4 books in
4C2 = 6 ways.

Last one will get 2 books in 2 remaining books in
1 ways.

So,
<edited>
3 ( 35 * 6 * 1) = 630 ways.
</edited>
Last edited by enniguy on Thu Aug 27, 2009 6:35 am, edited 2 times in total.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Mon Aug 10, 2009 6:19 am

Re: IMO 126

by csabiga » Thu Aug 27, 2009 3:41 am
enniguy wrote: So,
3 ( 35 + 6 + 1) = 126 ways.
These are not different situations.

The first student can get the books 35 ways AND after he/she got the books the second one can get from the others in 6 ways. Third student cannot choose.
You have to multiply the values.

3*(35*6*1) = 630 ways
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 5
Joined: Thu Aug 27, 2009 4:44 am

the answer

by [email protected] » Thu Aug 27, 2009 5:04 am
There are two selections : First of selecting the students and then selection of books.

Now we are not sure which student gets 2 books. So Let us choose which student gets 2 books. First student can be chosen in 3C1 way. Second student who gets 2 books can be chosen in 2C1 way. (as only 2 students remain for selection)

So there are 3C1 * 2C1 ways to choose students.

Now there are 7C2 ways to select 2 books given to student 1. And 5C2 ways to select 2 books to be given to student 2. And 3C3 ways to select 3 books to be given to student 3.

So total ways = 3C1 * 2C1 * 7C2 * 5C2 * 3C3 == 1260...

Let me know what is correct answer.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 40
Joined: Sat Feb 14, 2009 9:22 am
GMAT Score:460

Re: IMO 126

by GambitOS » Thu Aug 27, 2009 6:08 am
enniguy wrote:Last one will get 2 books in 2 remaining books in 1 ways.
Do you mean 2C2 or 2C1?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 156
Joined: Sat Jul 19, 2008 6:41 am
Thanked: 8 times

Re: IMO 126

by enniguy » Thu Aug 27, 2009 6:33 am
GambitOS wrote: Do you mean 2C2 or 2C1?
2C2. We need to select 2 books out of 2 books.

@csabiga: Thanks dude. I was wrong there. I have edited that post
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1