a question paper consists of 4 sections with 7 questions in each section.a candidate has to select 2 sections and has to solve 9 questions choosing atleast 3 from each of the selected sections.In how many ways can he answered the paper?
Answers
Given total number of sections = 4.
A candidate has to select 2 sections.
This can be happened in C(4,2) Ways.
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Given Total number of Questions in each section = 7.
That means total number of questions in 2 sections = 14.
In the given question he has to solve 9 questions choosing at least 3 from 2 sections.
(1) He can select 3 questions from section 1 and 6 questions from section 2.
= > C(7,3) * C(7,6)
(2) He can select 3 questions from section 2 and 6 questions from section 1.
= > C(7,3) * C(7,6)
(3) He can select 4 questions from section 1 and 5 questions from section 2.
= > C(7,4) * C(7,5)
(4) He can select 5 questions from section 2 and 4 from section 1.
= > C(7,5) * C(7,4).
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Therefore, total number of ways.
= > C(4,2) * (C(7,3) * C(7,6) + C(7,6) * C(7,3) + C(7,5) * C(7,4) + C(7,5) * C(7,4))
= > 6 * (35 * 7 + 7 * 35 + 21 * 35 + 21 * 35)
= > 6 * 1960
= > 11760.