Last visit was: 29 Apr 2026, 13:12 It is currently 29 Apr 2026, 13:12
Home
Messages
Tests
Schools
Events
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 29 Apr 2026
Posts: 109,975
Own Kudos:
811,975
 [2]
Given Kudos: 105,948
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: 109,975
Kudos: 811,975
 [2]
If the Board of Selectmen contains 4 positions, and if in the current 12 May 2023, 03:10
Kudos
Add Kudos
2
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:

25% (medium)

Question Stats:

73% (00:54) correct 27% (01:22) wrong based on 74 sessions

History

Date
Time
Result
Not Attempted Yet
If the Board of Selectmen contains 4 positions, and if in the current election two candidates are running for each position, then in how many different ways can these candidates be elected to the Board?

(A) 6
(B) 8
(C) 12
(D) 16
(E) 24
ShowHide Answer
Official Answer
D
User avatar
gmatophobia
User avatar
Quant Chat Moderator
Joined: 22 Dec 2016
Last visit: 19 Apr 2026
Posts: 3,173
Own Kudos:
11,484
 [1]
Given Kudos: 1,862
Location: India
Concentration: Strategy, Leadership
Posts: 3,173
Kudos: 11,484
 [1]
If the Board of Selectmen contains 4 positions, and if in the current 12 May 2023, 22:17
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If the Board of Selectmen contains 4 positions, and if in the current election two candidates are running for each position, then in how many different ways can these candidates be elected to the Board?

(A) 6
(B) 8
(C) 12
(D) 16
(E) 24
Show more

For each position on the board, we can have one of the two candidates elected. Therefore each position can be 'filled' in two ways. As there are four positions the number of ways to fill the four positions =

\(2 * 2 * 2 * 2 = 2^4 = 16\)

Option D
User avatar
Khwarizmi
User avatar
Joined: 19 Feb 2023
Last visit: 10 Jan 2024
Posts: 20
Own Kudos:
5
Given Kudos: 42
Posts: 20
Kudos: 5
If the Board of Selectmen contains 4 positions, and if in the current 29 Dec 2023, 08:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatophobia
Bunuel
If the Board of Selectmen contains 4 positions, and if in the current election two candidates are running for each position, then in how many different ways can these candidates be elected to the Board?

(A) 6
(B) 8
(C) 12
(D) 16
(E) 24

For each position on the board, we can have one of the two candidates elected. Therefore each position can be 'filled' in two ways. As there are four positions the number of ways to fill the four positions =

\(2 * 2 * 2 * 2 = 2^4 = 16\)

Option D
Show more

I do not conceptually understand this explanation. To me, the answer is not 2^4 but 4^2, the conceptual difference being that either of the two candidates can fill either of the four slots, thus, 4*4. The quoted explanation, however, says either of the four position can be filled by either of the two candidates but I do not think that is the case. Only two slots can be claimed by the two candidates, not all four.

Bunuel can you please help me understand?

EDIT: I thought the answer would be 4C2. Therefore, 4!/(2!2!) = 3*2 = 6. I got the wrong answer due to a conceptual gap.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 29 Apr 2026
Posts: 109,975
Own Kudos:
811,975
Given Kudos: 105,948
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: 109,975
Kudos: 811,975
If the Board of Selectmen contains 4 positions, and if in the current 29 Dec 2023, 08:25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Khwarizmi
gmatophobia
Bunuel
If the Board of Selectmen contains 4 positions, and if in the current election two candidates are running for each position, then in how many different ways can these candidates be elected to the Board?

(A) 6
(B) 8
(C) 12
(D) 16
(E) 24

For each position on the board, we can have one of the two candidates elected. Therefore each position can be 'filled' in two ways. As there are four positions the number of ways to fill the four positions =

\(2 * 2 * 2 * 2 = 2^4 = 16\)

Option D

I do not conceptually understand this explanation. To me, the answer is not 2^4 but 4^2, the conceptual difference being that either of the two candidates can fill either of the four slots, thus, 4*4. The quoted explanation, however, says either of the four position can be filled by either of the two candidates but I do not think that is the case. Only two slots can be claimed by the two candidates, not all four.

Bunuel can you please help me understand?

EDIT: I thought the answer would be 4C2. Therefore, 4!/(2!2!) = 3*2 = 6. I got the wrong answer due to a conceptual gap.
Show more

There are 4 positions to be filled, and for each position, there are two candidates competing:

    A and B are running for the first slot.
    C and D are running for the second slot.
    E and F are running for the third slot.
    G and H are running for the fourth slot.

To determine the total number of ways these candidates can be elected to the Board, we simply multiply the options for each slot together:

Total ways = 2 (options for the first slot) * 2 (options for the second slot) * 2 (options for the third slot) * 2 (options for the fourth slot) = 2^4 = 16

Does this make sense?
User avatar
Khwarizmi
User avatar
Joined: 19 Feb 2023
Last visit: 10 Jan 2024
Posts: 20
Own Kudos:
5
Given Kudos: 42
Posts: 20
Kudos: 5
If the Board of Selectmen contains 4 positions, and if in the current 29 Dec 2023, 10:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Khwarizmi
gmatophobia


For each position on the board, we can have one of the two candidates elected. Therefore each position can be 'filled' in two ways. As there are four positions the number of ways to fill the four positions =

\(2 * 2 * 2 * 2 = 2^4 = 16\)

Option D

I do not conceptually understand this explanation. To me, the answer is not 2^4 but 4^2, the conceptual difference being that either of the two candidates can fill either of the four slots, thus, 4*4. The quoted explanation, however, says either of the four position can be filled by either of the two candidates but I do not think that is the case. Only two slots can be claimed by the two candidates, not all four.

Bunuel can you please help me understand?

EDIT: I thought the answer would be 4C2. Therefore, 4!/(2!2!) = 3*2 = 6. I got the wrong answer due to a conceptual gap.

There are 4 positions to be filled, and for each position, there are two candidates competing:

    A and B are running for the first slot.
    C and D are running for the second slot.
    E and F are running for the third slot.
    G and H are running for the fourth slot.

To determine the total number of ways these candidates can be elected to the Board, we simply multiply the options for each slot together:

Total ways = 2 (options for the first slot) * 2 (options for the second slot) * 2 (options for the third slot) * 2 (options for the fourth slot) = 2^4 = 16

Does this make sense?
Show more

It does. Thanks a lot! I misunderstood the question, thinking two people, A and B, were competing over four positions.
User avatar
Paras96
User avatar
Joined: 11 Sep 2022
Last visit: 30 Dec 2023
Posts: 455
Own Kudos:
338
Given Kudos: 2
Location: India
Paras: Bhawsar
GMAT 1: 590 Q47 V24
GMAT 2: 580 Q49 V21
GMAT 3: 700 Q49 V35
GPA: 3.2
WE:Project Management (Other)
GMAT 3: 700 Q49 V35
Posts: 455
Kudos: 338
If the Board of Selectmen contains 4 positions, and if in the current 30 Dec 2023, 09:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If the Board of Selectmen contains 4 positions, and if in the current election two candidates are running for each position, then in how many different ways can these candidates be elected to the Board?
Sol=> for each of the 4 positions the position can be filled in two positions each so ,
2*2*2*2 = 2^4 ways
= 16
hence option D
Moderators:
Bunuel
Math Expert
109974 posts
Krunaal
Tuck School Moderator
852 posts