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In an examination, the question paper contains three different sections A, B and C containing 4, 5 and 6 questions respectively. In how many ways, a candidate can make a selection of 7 questions, selecting at least two questions from each section?
- a)890
- b)1420
- c)2700
- d)3140
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
In an examination, the question paper contains three different section...
Various ways of doing this is as follows:
Now do the selections.
This question is part of UPSC exam. View all Quant courses
Most Upvoted Answer
In an examination, the question paper contains three different section...
Total Number of Questions and Selection
There are a total of 15 questions in the question paper, with 4 in section A, 5 in section B and 6 in section C. The candidate needs to select a total of 7 questions, with at least 2 questions from each section.
Approach
We can approach this problem by breaking it down into cases.
Case 1: Selecting 2 questions from section A, 2 questions from section B and 3 questions from section C
We can select 2 questions from section A in 4C2 ways, 2 questions from section B in 5C2 ways and 3 questions from section C in 6C3 ways. The total number of ways of selecting 7 questions in this case is:
4C2 x 5C2 x 6C3 = 1800
Case 2: Selecting 2 questions from section A, 3 questions from section B and 2 questions from section C
We can select 2 questions from section A in 4C2 ways, 3 questions from section B in 5C3 ways and 2 questions from section C in 6C2 ways. The total number of ways of selecting 7 questions in this case is:
4C2 x 5C3 x 6C2 = 900
Case 3: Selecting 3 questions from section A, 2 questions from section B and 2 questions from section C
We can select 3 questions from section A in 4C3 ways, 2 questions from section B in 5C2 ways and 2 questions from section C in 6C2 ways. The total number of ways of selecting 7 questions in this case is:
4C3 x 5C2 x 6C2 = 540
Total Number of Ways
The total number of ways of selecting 7 questions with at least 2 questions from each section is the sum of the number of ways in each case:
1800 + 900 + 540 = 3240
However, we need to subtract the cases where we select only 1 question from one of the sections. We can select 1 section in 3C1 ways and then select 1 question from that section in the remaining questions (7-1=6) in the remaining sections in 9C6 ways. The total number of ways of selecting 7 questions with only 1 question from one of the sections is:
3C1 x 9C6 = 189
Therefore, the total number of ways of selecting 7 questions with at least 2 questions from each section is:
3240 - 189 = 2701
Answer
The correct answer is option (c) 2700.
There are a total of 15 questions in the question paper, with 4 in section A, 5 in section B and 6 in section C. The candidate needs to select a total of 7 questions, with at least 2 questions from each section.
Approach
We can approach this problem by breaking it down into cases.
Case 1: Selecting 2 questions from section A, 2 questions from section B and 3 questions from section C
We can select 2 questions from section A in 4C2 ways, 2 questions from section B in 5C2 ways and 3 questions from section C in 6C3 ways. The total number of ways of selecting 7 questions in this case is:
4C2 x 5C2 x 6C3 = 1800
Case 2: Selecting 2 questions from section A, 3 questions from section B and 2 questions from section C
We can select 2 questions from section A in 4C2 ways, 3 questions from section B in 5C3 ways and 2 questions from section C in 6C2 ways. The total number of ways of selecting 7 questions in this case is:
4C2 x 5C3 x 6C2 = 900
Case 3: Selecting 3 questions from section A, 2 questions from section B and 2 questions from section C
We can select 3 questions from section A in 4C3 ways, 2 questions from section B in 5C2 ways and 2 questions from section C in 6C2 ways. The total number of ways of selecting 7 questions in this case is:
4C3 x 5C2 x 6C2 = 540
Total Number of Ways
The total number of ways of selecting 7 questions with at least 2 questions from each section is the sum of the number of ways in each case:
1800 + 900 + 540 = 3240
However, we need to subtract the cases where we select only 1 question from one of the sections. We can select 1 section in 3C1 ways and then select 1 question from that section in the remaining questions (7-1=6) in the remaining sections in 9C6 ways. The total number of ways of selecting 7 questions with only 1 question from one of the sections is:
3C1 x 9C6 = 189
Therefore, the total number of ways of selecting 7 questions with at least 2 questions from each section is:
3240 - 189 = 2701
Answer
The correct answer is option (c) 2700.
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In an examination, the question paper contains three different sections A, B and C containing 4, 5 and 6 questions respectively. In how many ways, a candidate can make a selection of 7 questions, selecting at least two questions from each section?a)890b)1420c)2700d)3140Correct answer is option 'C'. Can you explain this answer?
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In an examination, the question paper contains three different sections A, B and C containing 4, 5 and 6 questions respectively. In how many ways, a candidate can make a selection of 7 questions, selecting at least two questions from each section?a)890b)1420c)2700d)3140Correct 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 an examination, the question paper contains three different sections A, B and C containing 4, 5 and 6 questions respectively. In how many ways, a candidate can make a selection of 7 questions, selecting at least two questions from each section?a)890b)1420c)2700d)3140Correct 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 an examination, the question paper contains three different sections A, B and C containing 4, 5 and 6 questions respectively. In how many ways, a candidate can make a selection of 7 questions, selecting at least two questions from each section?a)890b)1420c)2700d)3140Correct answer is option 'C'. Can you explain this answer?.
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