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 →

Permutations

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 966
Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members
Thanked: 230 times
by shankar.ashwin » Wed Sep 07, 2011 6:02 am
How many 6 letter word can be formed such that there are 2 vowels and 4 consonants in it when
(1) Repetition is not allowed
(2) Repetition is allowed.

I have seen a similar sum in the forum, but could anyone help me out in the case when repetition is allowed?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Quantitative Reasoning |
User avatar
Legendary Member
Posts: 1309
Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members
Location: India
Thanked: 310 times
GMAT Score:750

by cans » Wed Sep 07, 2011 6:49 am
a) 5C2*21C4*6! (select 2 vowels and 4 consonants and arrange them)
b) case 1: no repetition: 5C2*21C4*6!
case 2: only vowels repeated: 5C1*21C4*(6!/2!)
case 3: 2 consonants repeated (bbcd...): 5C2*21C3*(6!/2!)
case 4: 3 consonants repeated (bbbc): 5C2*21C2*6!/3!
case 5: 4 consonants (bbbb): 5C2*21C1*(6!/4!)
case 6: (bbcc): 5C2*21C2*(6!/2!/2!)
case 7: combo of case 2 and case 3. - 5C1*21C3*(6!/2!/2!)
case 8: case 2 + case 4
case 9: case 2+ case 5
case 10: case 2 + case 6
If my post helped you- let me know by pushing the thanks button ;)

Contact me about long distance tutoring!
[email protected]

Cans!!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 966
Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members
Thanked: 230 times

by shankar.ashwin » Wed Sep 07, 2011 7:37 am
Wow, thanks. I couldnt comprehend all the cases, but I get what you are doing. Unlikely to see a sum like this. But helpful to get your concepts right. Thanks
cans wrote:a) 5C2*21C4*6! (select 2 vowels and 4 consonants and arrange them)
b) case 1: no repetition: 5C2*21C4*6!
case 2: only vowels repeated: 5C1*21C4*(6!/2!)
case 3: 2 consonants repeated (bbcd...): 5C2*21C3*(6!/2!)
case 4: 3 consonants repeated (bbbc): 5C2*21C2*6!/3!
case 5: 4 consonants (bbbb): 5C2*21C1*(6!/4!)
case 6: (bbcc): 5C2*21C2*(6!/2!/2!)
case 7: combo of case 2 and case 3. - 5C1*21C3*(6!/2!/2!)
case 8: case 2 + case 4
case 9: case 2+ case 5
case 10: case 2 + case 6
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1