Last visit was: 17 Jul 2025, 12:29 It is currently 17 Jul 2025, 12:29
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
705-805 Level|   Probability|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,603
Own Kudos:
742,257
 [16]
Given Kudos: 98,220
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,603
Kudos: 742,257
 [16]
A box contains 10 cards numbered 1 through 10. If 3 cards are picked o 28 Jan 2022, 07:13
1
Kudos
Add Kudos
15
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

55% (02:02) correct 45% (02:03) wrong based on 231 sessions

History

Date
Time
Result
Not Attempted Yet
A box contains 10 cards numbered 1 through 10. If 3 cards are picked out randomly, without replacement, then what is the probability that 5 is the smallest value picked ?

A. 3/10
B. 1/6
C. 1/10
D. 1/12
E. 1/20

Experience a GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests
ShowHide Answer
Official Answer
D
User avatar
sujoykrdatta
User avatar
Joined: 26 Jun 2014
Last visit: 16 Jul 2025
Posts: 539
Own Kudos:
1,045
 [2]
Given Kudos: 13
Status:Mentor & Coach | GMAT Q51 | CAT 99.98
Expert
Expert reply
Posts: 539
Kudos: 1,045
 [2]
A box contains 10 cards numbered 1 through 10. If 3 cards are picked o 30 Jan 2022, 02:49
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel
A box contains 10 cards numbered 1 through 10. If 3 cards are picked out randomly, without replacement, then what is the probability that 5 is the smallest value picked ?

A. 3/10
B. 1/6
C. 1/10
D. 1/12
E. 1/20


We need to pick 3 cards with 5 as the least number.
Let us pick 5 first.
We now need to pick any 2 numbers from 6 to 10, i.e. 5 numbers
Number of favourable ways = 5C2 = 10


Total ways of choosing any 3 numbers = 10C3 = 120

Probability = 10/120 = 1/12

Note: we didn't consider arrangement in either numerator or denominator. If we did, it would be:
Favourable cases = 5C2 x 3! = 60
Total cases = 10 x 9 x 8 = 720
Probability = 60/720 = 1/12

Answer D

Posted from my mobile device
User avatar
adv95
User avatar
Joined: 23 Feb 2025
Last visit: 17 Jul 2025
Posts: 29
Own Kudos:
1
Given Kudos: 275
Posts: 29
Kudos: 1
A box contains 10 cards numbered 1 through 10. If 3 cards are picked o Updated on: 02 Jun 2025, 04:21
Originally posted by adv95 on 02 Jun 2025, 01:57.
Last edited by adv95 on 02 Jun 2025, 04:21, edited 2 times in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
A box contains 10 cards numbered 1 through 10. If 3 cards are picked out randomly, without replacement, then what is the probability that 5 is the smallest value picked ?

A. 3/10
B. 1/6
C. 1/10
D. 1/12
E. 1/20

Experience a GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests

Probability of selecting 5 in any of the three cards = 1/10
Probability of selecting 2 higher cards - 6 7 8 9 10 = 5/9 x 4/8
But we can draw 5 in any sequence, 1st 2nd or 3rd, therefore :
Prob. = 3 x 1/10 x 5/9 x 4/8 = 1/12
User avatar
Praveena_10
User avatar
Joined: 01 Jan 2024
Last visit: 17 Jul 2025
Posts: 33
Own Kudos:
33
Given Kudos: 21
Location: India
Schools: INSEAD Jan '26 ISB '26 HEC Sept '26 Kellogg '26 LBS '26 Stern '26
GPA: 7.3
Products:
GMAT Club Tests
Schools: INSEAD Jan '26 ISB '26 HEC Sept '26 Kellogg '26 LBS '26 Stern '26
Posts: 33
Kudos: 33
A box contains 10 cards numbered 1 through 10. If 3 cards are picked o 02 Jun 2025, 03:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello,
there are total 6 cards which are greater than or equal to 5. should the answer be 6/10*5/9*4/8=1/6.

Correct me if i am wrong.
adv95
Bunuel
A box contains 10 cards numbered 1 through 10. If 3 cards are picked out randomly, without replacement, then what is the probability that 5 is the smallest value picked ?

A. 3/10
B. 1/6
C. 1/10
D. 1/12
E. 1/20

Experience a GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests

If we select 3 cards numbered 5-10 from 10 cards numbered 1-10, simultaneously;
Probability of selecting these 3 nums from 5-10 : 5/10 x 4/9 x 3/8 = 1/12 => D
User avatar
Krunaal
User avatar
PS Forum Moderator
Joined: 15 Feb 2021
Last visit: 17 Jul 2025
Posts: 697
Own Kudos:
730
 [1]
Given Kudos: 243
Status:Under the Square and Compass
Location: India
WE:Marketing (Internet and New Media)
Products:
My Reviews GMAT Club Tests Forum Quiz
Posts: 697
Kudos: 730
 [1]
A box contains 10 cards numbered 1 through 10. If 3 cards are picked o 02 Jun 2025, 04:05
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Praveena_10
Hello,
there are total 6 cards which are greater than or equal to 5. should the answer be 6/10*5/9*4/8=1/6.

Correct me if i am wrong.
adv95
Bunuel
A box contains 10 cards numbered 1 through 10. If 3 cards are picked out randomly, without replacement, then what is the probability that 5 is the smallest value picked ?

A. 3/10
B. 1/6
C. 1/10
D. 1/12
E. 1/20

Experience a GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests

If we select 3 cards numbered 5-10 from 10 cards numbered 1-10, simultaneously;
Probability of selecting these 3 nums from 5-10 : 5/10 x 4/9 x 3/8 = 1/12 => D
No, because we need to pick 5 - from your solution a case may arise where 3 cards don't include 5 at all.

So with 5 already picked, we need to pick 2 cards from 6 to 10 => 5C2 ways = 10 ways. And total ways to select 3 cards from 10 = 10C3 = 120 ways. Therefore, probability = 10/120 = 1/12. Hope it helps.
User avatar
adv95
User avatar
Joined: 23 Feb 2025
Last visit: 17 Jul 2025
Posts: 29
Own Kudos:
1
Given Kudos: 275
Posts: 29
Kudos: 1
A box contains 10 cards numbered 1 through 10. If 3 cards are picked o 02 Jun 2025, 04:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Apologies, my approach was wrong.
corrected!
Praveena_10
Hello,
there are total 6 cards which are greater than or equal to 5. should the answer be 6/10*5/9*4/8=1/6.

Correct me if i am wrong.
adv95
Bunuel
A box contains 10 cards numbered 1 through 10. If 3 cards are picked out randomly, without replacement, then what is the probability that 5 is the smallest value picked ?

A. 3/10
B. 1/6
C. 1/10
D. 1/12
E. 1/20

Experience a GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests

If we select 3 cards numbered 5-10 from 10 cards numbered 1-10, simultaneously;
Probability of selecting these 3 nums from 5-10 : 5/10 x 4/9 x 3/8 = 1/12 => D
User avatar
demawtf
User avatar
Joined: 18 Mar 2024
Last visit: 17 Jul 2025
Posts: 51
Own Kudos:
60
Given Kudos: 518
Posts: 51
Kudos: 60
A box contains 10 cards numbered 1 through 10. If 3 cards are picked o 07 Jun 2025, 08:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
A box contains 10 cards numbered 1 through 10. If 3 cards are picked out randomly, without replacement, then what is the probability that 5 is the smallest value picked ?

A. 3/10
B. 1/6
C. 1/10
D. 1/12
E. 1/20

Without replacement + randomly = combinations scenario
Total outcomes = 10//7!*3!=120
Desired outcomes = 5 is picked for sure but needs to be the smallest, so the other numbers remaining for the 2 cards are 6,7,8,9,10 so 2 cards should be picked out of 5 desired numbers, again let's apply the combination formula 5!/3!*2! = 10

desired/tot=10/120 so 1/12 and answer is D.
User avatar
AnishTrivedi99
User avatar
Joined: 04 Nov 2024
Last visit: 02 Jul 2025
Posts: 4
Own Kudos:
1
Given Kudos: 32
Posts: 4
Kudos: 1
A box contains 10 cards numbered 1 through 10. If 3 cards are picked o 08 Jun 2025, 03:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
We need 5 to be the smallest -

Selecting 3 cards - select '5' in 1c1 ways

Then, for the remaining 2 - we can only select from 6, 7, 8, 9, 10 - so 5c2 ways

Total number of ways for selecting 3 cards out of 10 - 10c3 ways

Probability = 1c1*5c2 / 10c3 = 1/12
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 17 Jul 2025
Posts: 6,377
Own Kudos:
15,602
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,377
Kudos: 15,602
A box contains 10 cards numbered 1 through 10. If 3 cards are picked o 08 Jun 2025, 05:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
total ways of picking 3 card out of 10 = 10C3 = 120 (Refer video to understand better why?)

Favorable outcomes = 3 cards with smallest numbe 5
i.e. Card 5 has to be picked for sure and two more cards should be picked from {6, 7, 8, 9, 10}
so ways to pick 2 out of these 5 cards = 5C2 = 10

Probability = 5C2/10C3 = 10/120 = 1/12

Answer: Option D

Related Video:


Bunuel
A box contains 10 cards numbered 1 through 10. If 3 cards are picked out randomly, without replacement, then what is the probability that 5 is the smallest value picked ?

A. 3/10
B. 1/6
C. 1/10
D. 1/12
E. 1/20

Experience a GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests
Moderators:
Bunuel
Math Expert
102603 posts
Krunaal
PS Forum Moderator
697 posts