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11 Mar 2019, 10:59
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
76% (02:53) correct
24%
(02:47)
wrong
based on 147
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A question paper has 6 multiple choice questions. First 3 questions have 4 options each, and next 3 questions have 5 options each. Only 1 option can be selected for any question. In how many ways can david answer the question paper if :
1) David has to answer all questions
2) David has to ansWer first 2 question and remaining he can choose not to answer
A 6000, 17690
B 7000, 17280
C 8000, 18900
D 8000, 17280
E 5500, 15670
1) David has to answer all questions
2) David has to ansWer first 2 question and remaining he can choose not to answer
A 6000, 17690
B 7000, 17280
C 8000, 18900
D 8000, 17280
E 5500, 15670
11 Mar 2019, 11:23
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1) David has to answer all the questions.
First 3 questions. 4 ways each. 4*4*4 = 64 ways.
Next 3 questions. 5 ways each. 5*5*5 = 125 ways.
Total = 64*125 = 8000 ways.
Eliminate A, B and E.
2) David has to answer the first 2 questions. Total ways are 16 ways.
Now check the options D and C. Only 17280 is divisible by 16.
Hence D has to be the answer.
First 3 questions. 4 ways each. 4*4*4 = 64 ways.
Next 3 questions. 5 ways each. 5*5*5 = 125 ways.
Total = 64*125 = 8000 ways.
Eliminate A, B and E.
2) David has to answer the first 2 questions. Total ways are 16 ways.
Now check the options D and C. Only 17280 is divisible by 16.
Hence D has to be the answer.
11 Mar 2019, 20:37
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Solution
Given:
- • A question paper has 6 multiple choice questions.
• First 3 questions have 4 options each.
• Next 3 questions have 5 options each.
• Only 1 option can be selected for any question.
To find:
- • How many ways David can answer the question paper, if:
- o David has to answer all questions
o And, David has to answer first 2 question and remaining he can choose not to answer
Approach and Working:
Question 1:
For the first 3 questions, each question has 4 choices.
For the next 3 questions, each question has 5 choices.
- • As David has to answer all the questions, he can do so in 4 * 4 * 4 * 5 * 5 * 5 = 8000 ways.
Question 2:
For the first 2 questions, each question has 4 choices.
For the 3rd question, the question has 5 choices (not answering is also a choice).
For the next 3 questions, each question has 6 choices (not answering is also a choice).
- • Therefore, the number of ways David can answer the paper = 4 * 4 * 5 * 6 * 6 * 6 = 17280 ways
Hence, the correct answer is option D.
Answer: D
