Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
May 1308:30 AM PDT
-09:30 AM PDT
In Episode 4 of our GMAT Ninja CR series, we tackle the most intimidating CR question type: Boldface & "Legalese" questions. If you've ever stared at an answer choice that reads, "The first is a consideration introduced to counter a position that...- May 12
07:30 AM PDT
-08:30 AM PDT
Join the Live and learn more about Picking the Right Schools 
May 1212:00 PM EDT
-11:59 PM EDT
Make the most of your break with the most realistic GMAT™ prep. Take up to $700 off select products.- May 14
08:30 AM PDT
-09:30 AM PDT
Most GMAT test-takers are intimidated by the hardest GMAT Verbal questions. In this session, Target Test Prep GMAT instructor Erika Tyler-John, a 100th percentile GMAT scorer, will show you how top scorers break down challenging Verbal questions.. - Jun 10
06:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..
31 Jul 2025, 10:04
Kudos
Bookmarks
Each of \(n\) people randomly selects an integer from 1 to \(n\), inclusive. If the probability that all of them choose different numbers is six times the probability that all of them choose the same number, what is the value of \(n\)?
A. 3
B. 4
C. 5
D. 6
E. 8
A. 3
B. 4
C. 5
D. 6
E. 8
31 Jul 2025, 10:04
Kudos
Bookmarks
Official Solution:
Each of \(n\) people randomly selects an integer from 1 to \(n\), inclusive. If the probability that all of them choose different numbers is six times the probability that all of them choose the same number, what is the value of \(n\)?
A. 3
B. 4
C. 5
D. 6
E. 8
Each person has \(n\) options, integers from 1 to \(n\), inclusive. So the total number of possible outcomes (denominator) is \(n^n\) in all cases.
1. All choose different numbers:
The number of ways to assign \(n\) different numbers \((1, 2, ..., n)\) to \(n\) people is \(n!\)
So probability \(= \frac{n!}{n^n}\)
2. All choose the same number:
This can happen in exactly \(n\) ways: all choose 1, all choose 2, ..., all choose \(n\)
So probability \(= \frac{n}{n^n}\)
We are given:
\(\frac{n!}{n^n} = 6 * (\frac{n}{n^n})\)
Cancel denominator:
\(n! = 6n\)
Substituting the answer choices, we see that only \(n = 4\) satisfies the equation: \(4! = 6 *4 = 24\).
Answer: B
Each of \(n\) people randomly selects an integer from 1 to \(n\), inclusive. If the probability that all of them choose different numbers is six times the probability that all of them choose the same number, what is the value of \(n\)?
A. 3
B. 4
C. 5
D. 6
E. 8
Each person has \(n\) options, integers from 1 to \(n\), inclusive. So the total number of possible outcomes (denominator) is \(n^n\) in all cases.
1. All choose different numbers:
The number of ways to assign \(n\) different numbers \((1, 2, ..., n)\) to \(n\) people is \(n!\)
So probability \(= \frac{n!}{n^n}\)
2. All choose the same number:
This can happen in exactly \(n\) ways: all choose 1, all choose 2, ..., all choose \(n\)
So probability \(= \frac{n}{n^n}\)
We are given:
\(\frac{n!}{n^n} = 6 * (\frac{n}{n^n})\)
Cancel denominator:
\(n! = 6n\)
Substituting the answer choices, we see that only \(n = 4\) satisfies the equation: \(4! = 6 *4 = 24\).
Answer: B
22 Mar 2026, 01:52
Kudos
Bookmarks
Hi Bunuel,
I have solved using this method my approach was correct or not?
i have solved using options
Probability of different is = 6 * probability of same
Probability of different is: i took 4 from option is 1/4*3/4*2/4*1/4
probability of same from 4 different is 1/4*1/4*1/4*1/4
we are also getting answer as Probability of different is = 6 * probability of same
I have solved using this method my approach was correct or not?
i have solved using options
Probability of different is = 6 * probability of same
Probability of different is: i took 4 from option is 1/4*3/4*2/4*1/4
probability of same from 4 different is 1/4*1/4*1/4*1/4
we are also getting answer as Probability of different is = 6 * probability of same
Bunuel
