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07 Sep 2026, 14:03
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
67% (02:07) correct
33%
(02:55)
wrong
based on 46
sessions
History
Date
Time
Result
Not Attempted Yet
A candidate is required to answer-to-answer seven questions out of twelve questions, which are divided into two groups each containing six questions. He is not permitted to attempt more than five questions from each group. In how many ways can be choose the questions?
A. 480
B. 680
C. 780
D. 980
E. 1420
A. 480
B. 680
C. 780
D. 980
E. 1420
08 Sep 2026, 20:48
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Constraints: need 7 questions with <= 5 questions from each group
There are 2 possible cases.
Case 1: 5 questions from one group and 2 questions from the other
Case 2: 4 questions from one group and 3 questions from the other
Case 1
Since we have 2 groups, there are 2 ways to decide which group to do 5 questions. Then we need to choose 5 questions out of 6 questions from that group, and choose 2 questions out of 6 questions from the other.
2 * 6C5 * 6C2 = 180
Case 2
Same concept, just different numbers
2 * 6C4 * 6C3 = 600
There are 780 ways.
Answer: C
There are 2 possible cases.
Case 1: 5 questions from one group and 2 questions from the other
Case 2: 4 questions from one group and 3 questions from the other
Case 1
Since we have 2 groups, there are 2 ways to decide which group to do 5 questions. Then we need to choose 5 questions out of 6 questions from that group, and choose 2 questions out of 6 questions from the other.
2 * 6C5 * 6C2 = 180
Case 2
Same concept, just different numbers
2 * 6C4 * 6C3 = 600
There are 780 ways.
Answer: C
20 Sep 2026, 08:58
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any other way to solve
zaturn
