CA Foundation Exam > CA Foundation Questions > In your office 4 posts have fallen vacant. In...
Start Learning for Free
In your office 4 posts have fallen vacant. In how many ways a selection out of 31 candidates can be made if one candidate is always included?
- a)30C3
- b)30C4
- c)31C3
- d)31C4
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In your office 4 posts have fallen vacant. In how many ways a selectio...
4 posts,31 candidates .out of which 1 always included..from the 4 positions 1 position filled rest 3 positions also from 31 candidates 1 always included rest 30 candidates therefore we can arrange 30 candidates in 3 positions so,30c3
Free Test
FREE
| Start Free Test |
Community Answer
In your office 4 posts have fallen vacant. In how many ways a selectio...
To solve this problem, we need to use the concept of combinations.
Given:
- There are 31 candidates in total.
- 4 posts have fallen vacant.
- One candidate is always included in the selection.
We need to find the number of ways a selection can be made out of the 31 candidates, considering that one candidate is always included.
Solution:
Step 1: Select the candidate who is always included
Since one candidate is always included, we have only one choice for this candidate.
Number of ways to select the candidate who is always included = 1
Step 2: Select the remaining candidates for the vacant posts
Out of the remaining candidates (31 - 1 = 30), we need to select candidates for the 4 vacant posts.
Number of ways to select the remaining candidates = 30C3
(30C3 represents selecting 3 candidates out of 30)
Step 3: Multiply the number of ways from Step 1 and Step 2
To find the total number of ways to make a selection, we need to multiply the number of ways from Step 1 and Step 2.
Total number of ways = 1 * 30C3
Simplifying the expression:
30C3 = (30!)/(3!(30-3)!)
= (30!)/(3!27!)
Cancelling out common terms in the numerator and denominator:
= (30 * 29 * 28)/(3 * 2 * 1)
= 4060
Therefore, the correct answer is option 'A', which is 30C3.
Given:
- There are 31 candidates in total.
- 4 posts have fallen vacant.
- One candidate is always included in the selection.
We need to find the number of ways a selection can be made out of the 31 candidates, considering that one candidate is always included.
Solution:
Step 1: Select the candidate who is always included
Since one candidate is always included, we have only one choice for this candidate.
Number of ways to select the candidate who is always included = 1
Step 2: Select the remaining candidates for the vacant posts
Out of the remaining candidates (31 - 1 = 30), we need to select candidates for the 4 vacant posts.
Number of ways to select the remaining candidates = 30C3
(30C3 represents selecting 3 candidates out of 30)
Step 3: Multiply the number of ways from Step 1 and Step 2
To find the total number of ways to make a selection, we need to multiply the number of ways from Step 1 and Step 2.
Total number of ways = 1 * 30C3
Simplifying the expression:
30C3 = (30!)/(3!(30-3)!)
= (30!)/(3!27!)
Cancelling out common terms in the numerator and denominator:
= (30 * 29 * 28)/(3 * 2 * 1)
= 4060
Therefore, the correct answer is option 'A', which is 30C3.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
In your office 4 posts have fallen vacant. In how many ways a selection out of 31 candidates can be made if one candidate is always included?a)30C3b)30C4c)31C3d)31C4Correct answer is option 'A'. Can you explain this answer?
Question Description
In your office 4 posts have fallen vacant. In how many ways a selection out of 31 candidates can be made if one candidate is always included?a)30C3b)30C4c)31C3d)31C4Correct answer is option 'A'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about In your office 4 posts have fallen vacant. In how many ways a selection out of 31 candidates can be made if one candidate is always included?a)30C3b)30C4c)31C3d)31C4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In your office 4 posts have fallen vacant. In how many ways a selection out of 31 candidates can be made if one candidate is always included?a)30C3b)30C4c)31C3d)31C4Correct answer is option 'A'. Can you explain this answer?.
In your office 4 posts have fallen vacant. In how many ways a selection out of 31 candidates can be made if one candidate is always included?a)30C3b)30C4c)31C3d)31C4Correct answer is option 'A'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about In your office 4 posts have fallen vacant. In how many ways a selection out of 31 candidates can be made if one candidate is always included?a)30C3b)30C4c)31C3d)31C4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In your office 4 posts have fallen vacant. In how many ways a selection out of 31 candidates can be made if one candidate is always included?a)30C3b)30C4c)31C3d)31C4Correct answer is option 'A'. Can you explain this answer?.
Solutions for In your office 4 posts have fallen vacant. In how many ways a selection out of 31 candidates can be made if one candidate is always included?a)30C3b)30C4c)31C3d)31C4Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of In your office 4 posts have fallen vacant. In how many ways a selection out of 31 candidates can be made if one candidate is always included?a)30C3b)30C4c)31C3d)31C4Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In your office 4 posts have fallen vacant. In how many ways a selection out of 31 candidates can be made if one candidate is always included?a)30C3b)30C4c)31C3d)31C4Correct answer is option 'A'. Can you explain this answer?, a detailed solution for In your office 4 posts have fallen vacant. In how many ways a selection out of 31 candidates can be made if one candidate is always included?a)30C3b)30C4c)31C3d)31C4Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of In your office 4 posts have fallen vacant. In how many ways a selection out of 31 candidates can be made if one candidate is always included?a)30C3b)30C4c)31C3d)31C4Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In your office 4 posts have fallen vacant. In how many ways a selection out of 31 candidates can be made if one candidate is always included?a)30C3b)30C4c)31C3d)31C4Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup