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 and Combination Problem

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 202
Joined: Sun Sep 08, 2013 11:51 amFollowed by: 2 members
Thanked: 3 times
by sukhman » Mon Sep 09, 2013 10:35 pm
In a college, 8 students play at the State level and 10 at the National level. If 6 students play at both National and State levels, in how many ways can 9 students be selected from among these? 12C9
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 283
Joined: Sun Jun 23, 2013 11:56 pmFollowed by: 26 members
Location: Bangalore, India
Thanked: 97 times
GMAT Score:750

by ganeshrkamath » Mon Sep 09, 2013 11:59 pm
sukhman wrote:In a college, 8 students play at the State level and 10 at the National level. If 6 students play at both National and State levels, in how many ways can 9 students be selected from among these? 12C9
6 play at both levels
(8-6) = 2 play at only state level
(10-6) = 4 play at only national level
Total = 6 + 2 + 4 = 12
Select 9 out of 12 = 12C9

Cheers
Every job is a self-portrait of the person who did it. Autograph your work with excellence.

Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Tue Sep 10, 2013 6:49 am
ganeshrkamath's solution is perfect, and the answer is, indeed, 12C9
However, it's unlikely that the answer choices would be in the form xCy (since there are different ways to denote combinations). For this particular question, we'd probably have to evaluate 12C9. So, let's do that (quickly!!).

If anyone is interested, we have a free video on calculating combinations in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789

When calculating combinations (in our head), it's useful to know the following rule: nCr = nC(n-r). In other words, "n choose r" is equal to "n choose n-r"
So, for example: 10C7 = 10C3
8C7 = 8C1
20C18 = 20C2

This rule is useful because it's much easier to calculate combinations when the second value is smaller.

So, here 12C9 = 12C3
= (12)(11)(10)/(3)(2)(1)
= (2)(11)(10)
= 220

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1