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 →

Permutaion

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Mon Apr 18, 2011 4:34 pm
by SwatiDenre » Fri Jun 10, 2011 1:50 pm
How many five letter words can be formed by picking 3 vowels and 2 consonants from the word REACTION such that the two consonants always remain together?


A. 2170
B. 2336
C. 1800
D. 1152
E. 3054


Ans - D


How to solve this prob. Please help.
Thanks in advance.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Legendary Member
Posts: 1084
Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members
Thanked: 158 times

by pemdas » Fri Jun 10, 2011 2:08 pm
first of all, condition 'two consonants remain together' comes as ONE
in total, there are 4 consonants (R,C,T,N); when they come 'together' there are 4C2, 4!/(2!*2!)=6 combination sets

3 vowels out of 4 ones (E,A,I,O) come in 4C3, 4!/3!=4 combination sets

finally, five letter words when two (consonants) are fixed 'come together' makes 4 letter words indeed with the possibility of reversed consonants (RC-CR), hence 2 ways of 4 letter word combination sets. 4C1, 4!/1!=24 and 24*2=48

6*4*48=1152

SwatiDenre wrote:How many five letter words can be formed by picking 3 vowels and 2 consonants from the word REACTION such that the two consonants always remain together?


A. 2170
B. 2336
C. 1800
D. 1152
E. 3054


Ans - D


How to solve this prob. Please help.
Thanks in advance.
Success doesn't come overnight!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 26
Joined: Thu Jun 02, 2011 7:21 am

by finites » Fri Jun 10, 2011 2:17 pm
1152..

3 vowels can be selected like 4C3 = 4.
2 consonants = 4C2 = 6

5 letter word selection = 6 * 4 =24.

2 consonants must be together.ie c1c2.
3 vowels can be v1,v2,v3.
c1c2, v1,v2,v3 ie again 4 different possibilities = 4!
c1c2 can also be c2c1 ie 2 possibilities.

ie 2 * 4! orders with v1,v2,v3,v4 ,c1,c2..

5 letter selection * arranging order = 24*(2*24)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
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 » Fri Jun 10, 2011 7:53 pm
REACTION. No of consonants (C=) = 4
No. of vowels (V) = 4
select 3 vowels = 4C3 =4
select 2 consonants = 4C2 = 6
arrange (such that consonants remain together) = 4!*2! = 48
total = 4*6*48 = 24*48 = 1152
IMO D
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
Post new topic Post Reply
• Page 1 of 1