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 →

few permutation questions

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 273
Joined: Thu Sep 08, 2011 6:50 amFollowed by: 3 members
Thanked: 5 times
by fangtray » Mon Sep 19, 2011 8:49 pm
1. in how many ways can a committee of 2 boys and 3 girls can be made out of 5 boys and 6 girls?


2.there are 4 copies of 5 different books. in how many ways can they be arranged on a shelf?

3. in how many ways a three digit number can be written using all of the digits from 1 to 9 without repetition of any digit?

4. in how many ways can the letters of the word "missisippi" be arranged?


sorry guys i'm very bad at permutations and combinations... instead of just providing something like 7*6*5*4*3 can someone explain why they do it that way?

thanks for all of your help
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members
Location: Milpitas, CA
Thanked: 1854 times
GMAT Score:770

by Anurag@Gurome » Mon Sep 19, 2011 9:10 pm
In how many ways can a committee of 2 boys and 3 girls can be made out of 5 boys and 6 girls?
2 boys can be selected from 5 boys in 5C2 ways.
3 girls can be selected from 6 girls in 6C3 ways.
Therefore, required number of committees = 5C2 * 6C3 = 5!/(3! * 2!) * 6!/(3! * 3!) = 10 * 20 = 200
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members
Location: Milpitas, CA
Thanked: 1854 times
GMAT Score:770

by Anurag@Gurome » Mon Sep 19, 2011 9:17 pm
There are 4 copies of 5 different books. In how many ways can they be arranged on a shelf?
4 copies of 5 different books means in all there are 4 * 5 = 20 books, which can be arranged on the shelf in 20! ways
Therefore, no. of ways in which 4 copies of 5 different books can be arranged on a shelf = [spoiler]20!/(4!)^5[/spoiler]
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members
Location: Milpitas, CA
Thanked: 1854 times
GMAT Score:770

by Anurag@Gurome » Mon Sep 19, 2011 9:25 pm
In how many ways can the letters of the word "missisippi" be arranged?
No. of letters in the word "missisippi" = 10, which can be arranged in 10! ways
Now, no. of "s" = 3
No. of "i" = 4
No. of "p" = 2
Since the above letters are repeating, so we need to divide these repetitions.

Required no. of ways = 10!/(3! * 4! * 2!) = 10 * 9 * 8 * 7 * 6 * 5/(3! * 2!) = 10 * 9 * 4 * 7 * 5 = 12,600
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 425
Joined: Wed Dec 08, 2010 9:00 amFollowed by: 7 members
Thanked: 56 times
GMAT Score:690

by LalaB » Mon Sep 19, 2011 9:45 pm
fangtray wrote:
3. in how many ways a three digit number can be written using all of the digits from 1 to 9 without repetition of any digit?
9*8*7
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 425
Joined: Wed Dec 08, 2010 9:00 amFollowed by: 7 members
Thanked: 56 times
GMAT Score:690

by LalaB » Mon Sep 19, 2011 9:48 pm
Anurag@Gurome wrote:
There are 4 copies of 5 different books. In how many ways can they be arranged on a shelf?
4 copies of 5 different books means in all there are 4 * 5 = 20 books, which can be arranged on the shelf in 20! ways
Therefore, no. of ways in which 4 copies of 5 different books can be arranged on a shelf = [spoiler]20!/(4!)^5[/spoiler]
I thought the question asks all books arrangement, and got the answer 20!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 273
Joined: Thu Sep 08, 2011 6:50 amFollowed by: 3 members
Thanked: 5 times

by fangtray » Tue Sep 20, 2011 2:44 am
LalaB wrote:
fangtray wrote:
3. in how many ways a three digit number can be written using all of the digits from 1 to 9 without repetition of any digit?
9*8*7
thats what i thought at first. but its actually 9^3 ways. at least thats what is on the answer key. does somebody know?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 142
Joined: Mon Jan 10, 2011 8:03 am
Thanked: 19 times

by krishnasty » Tue Sep 20, 2011 3:38 am
fangtray wrote:
LalaB wrote:
fangtray wrote:
3. in how many ways a three digit number can be written using all of the digits from 1 to 9 without repetition of any digit?
9*8*7
thats what i thought at first. but its actually 9^3 ways. at least thats what is on the answer key. does somebody know?
It cant be 9^3..
The first digit can be filled by any number from 1-9...9 ways
the scond digit can be filled by any number EXCEPT the number chosen for the first digit..hence, 8 ways
similarly, for the 3rd digit, it has to be filled in 7 ways ( coz 2 numbers are already chosen).
total ways : 9*8*7

had it been that the number can be chosen with repetation too, then it would have been 9*9*9..
---------------------------------------
Appreciation in thanks please!!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 273
Joined: Thu Sep 08, 2011 6:50 amFollowed by: 3 members
Thanked: 5 times

by fangtray » Tue Sep 20, 2011 3:47 am
Anurag@Gurome wrote:
There are 4 copies of 5 different books. In how many ways can they be arranged on a shelf?
4 copies of 5 different books means in all there are 4 * 5 = 20 books, which can be arranged on the shelf in 20! ways
Therefore, no. of ways in which 4 copies of 5 different books can be arranged on a shelf = [spoiler]20!/(4!)^5[/spoiler]
why divide by 4!)^5?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 496
Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member
Thanked: 38 times

by sl750 » Tue Sep 20, 2011 6:13 am
fangtray wrote:
Anurag@Gurome wrote:
There are 4 copies of 5 different books. In how many ways can they be arranged on a shelf?
4 copies of 5 different books means in all there are 4 * 5 = 20 books, which can be arranged on the shelf in 20! ways
Therefore, no. of ways in which 4 copies of 5 different books can be arranged on a shelf = [spoiler]20!/(4!)^5[/spoiler]
why divide by 4!)^5?
I believe that is necessary to avoid repetition. It is like the missippii problem posted by you.
The four copies are identical. Since there are 5 different books each book has 4 copies, we divide
by 4!^5
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1