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 →

Permutation / combinations

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 60
Joined: Thu Sep 24, 2009 2:38 pmFollowed by: 9 members
Location: NYC
Thanked: 33 times
GMAT Score:710
by benjiboo » Thu Sep 24, 2009 7:05 pm
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be?






Why is the answer 35 (7!/3!x4!) and not 5^3 written like (5*5*5)=125?

Thank you
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 107
Joined: Tue Sep 15, 2009 7:18 pm
Location: Pune, India
Thanked: 6 times
GMAT Score:630

i'm puzzled

by vivekjaiswal » Thu Sep 24, 2009 7:23 pm
I would have gone for the 5*5*5
But as you say it isn't the right answer...I hope someone would clarify :(

I hope there isn't anything missing in the question
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 60
Joined: Thu Sep 24, 2009 2:38 pmFollowed by: 9 members
Location: NYC
Thanked: 33 times
GMAT Score:710

Re: i'm puzzled

by benjiboo » Thu Sep 24, 2009 7:35 pm
vivekjaiswal wrote:I would have gone for the 5*5*5
But as you say it isn't the right answer...I hope someone would clarify :(

I hope there isn't anything missing in the question

Nothing is missing in the question. Someone needs to clarify why you can not use the 5*5*5 formula. (n^r)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Thu Aug 27, 2009 3:40 am
Thanked: 2 times
GMAT Score:700

Re: Permutation / combinations

by Trader AK » Fri Sep 25, 2009 9:03 am
benjiboo wrote:There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be?

Why is the answer 35 (7!/3!x4!) and not 5^3 written like (5*5*5)=125?

Thank you
Question 1
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be? (flavors cannot be repeated)
Answer
5C3 = 5!/(3! x 2!) = 10

Question 2
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be? (flavors can be repeated)
Answer
5 x 5 x 5 = 125

Question 3
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be? (flavors can be repeated but order doesn't matter)
Answer
(5+3-1)! / [3! x (5-1)!] = 35

From GMAT point of view, you need to know only first and second questions.

I am sure, 3rd question is not from any reputed GMAT related material.

There are many things, Permutation with repetition, Permutation without repetition, Combination with repetition, Combination without repetition. GMAT doesn't ask all the things. This will become very very complicated.

Still if u want to do research on question number 3, you can do that (but not for your GMAT exam). This question is about "Combination without repetition". So, here we can do repetitions. But point to be noted is that it is a combination problem. So, order doesn't matter.
Normally, when we take 5^3, order matters. So, BBL and BLB are different possibilities. But in 3rd question, BBL & BLB are same only (because order doesn't matter). This way, we need to proceed.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Newbie | Next Rank: 10 Posts
Posts: 6
Joined: Thu Mar 20, 2008 5:05 pm
Location: Colorado Springs, CO
GMAT Score:550

by rajiishere » Fri Sep 25, 2009 9:23 am
I would have gone for 5*5*5 or would have thought that something on the question about repetition is missing...

But Trader AK, that was a detailed explanation...Thanks!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 60
Joined: Thu Sep 24, 2009 2:38 pmFollowed by: 9 members
Location: NYC
Thanked: 33 times
GMAT Score:710

by benjiboo » Fri Sep 25, 2009 9:31 am
Trader AK, thank you for the explanation.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 107
Joined: Tue Sep 15, 2009 7:18 pm
Location: Pune, India
Thanked: 6 times
GMAT Score:630

Re: Permutation / combinations

by vivekjaiswal » Mon Sep 28, 2009 7:29 pm
Trader AK wrote:
benjiboo wrote:There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be?

Why is the answer 35 (7!/3!x4!) and not 5^3 written like (5*5*5)=125?

Thank you
Question 1
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be? (flavors cannot be repeated)
Answer
5C3 = 5!/(3! x 2!) = 10

Question 2
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be? (flavors can be repeated)
Answer
5 x 5 x 5 = 125

Question 3
There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be? (flavors can be repeated but order doesn't matter)
Answer
(5+3-1)! / [3! x (5-1)!] = 35
From GMAT point of view, you need to know only first and second questions.

I am sure, 3rd question is not from any reputed GMAT related material.

There are many things, Permutation with repetition, Permutation without repetition, Combination with repetition, Combination without repetition. GMAT doesn't ask all the things. This will become very very complicated.

Still if u want to do research on question number 3, you can do that (but not for your GMAT exam). This question is about "Combination without repetition". So, here we can do repetitions. But point to be noted is that it is a combination problem. So, order doesn't matter.
Normally, when we take 5^3, order matters. So, BBL and BLB are different possibilities. But in 3rd question, BBL & BLB are same only (because order doesn't matter). This way, we need to proceed.
Hi Trader AK,

Thanks for showing us all the possible outcomes of various interpretations.
May be I am being really dumb, but could you please also explain how you arrived at the last expression (the one I have bold faced in the quote above.)

Thanks Again,
Vivek
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1