Quant Exam > Quant Questions > In a room there are 2 green chairs, 3 yellow ...
Start Learning for Free
In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?
- a)3
- b)30
- c)64
- d)84
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs....
Most Upvoted Answer
In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs....
To solve this problem, we can use the concept of combinations.
Step 1: Calculate the total number of ways to choose 3 chairs from all the available chairs
The total number of chairs in the room is 2 green chairs + 3 yellow chairs + 4 blue chairs = 9 chairs.
We need to choose 3 chairs from these 9 chairs, which can be done in C(9, 3) ways, where C(n, r) represents the number of combinations of choosing r items from a set of n items.
C(9, 3) = 9! / (3! * (9-3)!) = 9! / (3! * 6!) = (9 * 8 * 7) / (3 * 2 * 1) = 84 ways.
Step 2: Calculate the number of ways to choose 3 chairs without including any yellow chair
Since we want to find the number of ways to choose at least one yellow chair, we need to subtract the number of ways to choose 3 chairs without including any yellow chair from the total number of ways calculated in step 1.
To choose 3 chairs without including any yellow chair, we can choose from the green and blue chairs only.
The number of ways to choose 3 chairs from the green and blue chairs is C(2+4, 3) = C(6, 3) = 6! / (3! * (6-3)!) = 6! / (3! * 3!) = (6 * 5 * 4) / (3 * 2 * 1) = 20 ways.
Step 3: Calculate the number of ways to choose 3 chairs with at least one yellow chair
The number of ways to choose 3 chairs with at least one yellow chair is the total number of ways minus the number of ways calculated in step 2.
Number of ways = Total number of ways - Number of ways without yellow chair = 84 - 20 = 64 ways.
Therefore, the correct answer is option C) 64.
Step 1: Calculate the total number of ways to choose 3 chairs from all the available chairs
The total number of chairs in the room is 2 green chairs + 3 yellow chairs + 4 blue chairs = 9 chairs.
We need to choose 3 chairs from these 9 chairs, which can be done in C(9, 3) ways, where C(n, r) represents the number of combinations of choosing r items from a set of n items.
C(9, 3) = 9! / (3! * (9-3)!) = 9! / (3! * 6!) = (9 * 8 * 7) / (3 * 2 * 1) = 84 ways.
Step 2: Calculate the number of ways to choose 3 chairs without including any yellow chair
Since we want to find the number of ways to choose at least one yellow chair, we need to subtract the number of ways to choose 3 chairs without including any yellow chair from the total number of ways calculated in step 1.
To choose 3 chairs without including any yellow chair, we can choose from the green and blue chairs only.
The number of ways to choose 3 chairs from the green and blue chairs is C(2+4, 3) = C(6, 3) = 6! / (3! * (6-3)!) = 6! / (3! * 3!) = (6 * 5 * 4) / (3 * 2 * 1) = 20 ways.
Step 3: Calculate the number of ways to choose 3 chairs with at least one yellow chair
The number of ways to choose 3 chairs with at least one yellow chair is the total number of ways minus the number of ways calculated in step 2.
Number of ways = Total number of ways - Number of ways without yellow chair = 84 - 20 = 64 ways.
Therefore, the correct answer is option C) 64.
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?a)3b)30c)64d)84Correct answer is option 'C'. Can you explain this answer?
Question Description
In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?a)3b)30c)64d)84Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?a)3b)30c)64d)84Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?a)3b)30c)64d)84Correct answer is option 'C'. Can you explain this answer?.
In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?a)3b)30c)64d)84Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?a)3b)30c)64d)84Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?a)3b)30c)64d)84Correct answer is option 'C'. Can you explain this answer?.
Solutions for In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?a)3b)30c)64d)84Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?a)3b)30c)64d)84Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?a)3b)30c)64d)84Correct answer is option 'C'. Can you explain this answer?, a detailed solution for In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?a)3b)30c)64d)84Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?a)3b)30c)64d)84Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?a)3b)30c)64d)84Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup