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05 Jun 2020, 04:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
53% (02:41) correct
47%
(02:39)
wrong
based on 202
sessions
History
Date
Time
Result
Not Attempted Yet
A test contains 3 different sections , each sections has 5 questions. Minimum 2 questions need to be attempted from each section in such a way that total of 8 questions are attempted. In how many ways a student appearing in the test can attempt the 8 questions?
A. 36000
B. 6435
C. 6300
D. 4635
E. 4500
A. 36000
B. 6435
C. 6300
D. 4635
E. 4500
shameekv1989
GMAT 3: 720 Q50 V38
Posts: 816
05 Jun 2020, 04:14
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SkR1
2 Combinations possible :-
2,2,4 or 2,3,3
Case 1 :-
Choosing which one gets to select 4 - 3 ways
\(5_C_2 * 5_C_2 * 5_C_4 * 3\) = 10*10*5*3 = 1500
Case 2 :-
Choosing which one gets to select 2 - 3 ways
\(5_C_2 * 5_C_3 * 5_C_3 * 3\) = 10*10*10*3 = 3000
Total = 3000+1500 = 4500
Answer - E
General Discussion
05 Jun 2020, 04:19
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There are two distinct ways a test taker could complete a total of 8 questions, while completing at least 2 from each section:
• complete 4 from one section, and 2 from the other two sections
• complete 2 from one section, and 3 from the other two sections
If the test taker will complete 4 questions from one section, she has 5 choices (5C4 if you like) for which questions to do. She then has 5C2 = (5)(4)/2! = 10 choices for each of the other two sections. Since there are three choices for which section to do the four questions from, there are (3)(5)(10)(10) = 1500 ways to complete four questions from one section, and two from the other sections.
Similarly, if the test taker will do 2 questions from one section, she has 5C2 = 10 choices for those questions. For the two sections where she completes 3 questions, she has 5C3 = (5)(4)(3)/3! = 10 choices. Since she has three choices for the section from which to complete the two questions, there are (3)(10)(10)(10) = 3000 ways to complete two questions from one section, and three from the other sections.
Adding the results from each case, the answer is 1500+3000 = 4500.
• complete 4 from one section, and 2 from the other two sections
• complete 2 from one section, and 3 from the other two sections
If the test taker will complete 4 questions from one section, she has 5 choices (5C4 if you like) for which questions to do. She then has 5C2 = (5)(4)/2! = 10 choices for each of the other two sections. Since there are three choices for which section to do the four questions from, there are (3)(5)(10)(10) = 1500 ways to complete four questions from one section, and two from the other sections.
Similarly, if the test taker will do 2 questions from one section, she has 5C2 = 10 choices for those questions. For the two sections where she completes 3 questions, she has 5C3 = (5)(4)(3)/3! = 10 choices. Since she has three choices for the section from which to complete the two questions, there are (3)(10)(10)(10) = 3000 ways to complete two questions from one section, and three from the other sections.
Adding the results from each case, the answer is 1500+3000 = 4500.
