An examination paper consists of 12 questions divided into two parts A and B. Part A contains 7 questions and part B contains 5 questions. A candidate is required to attempt 8 questions selecting at least 3 from each part, in how many maximum ways can the candidate select the questions?
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There are 5 question in parts & 7 question in parts 2
atleast 8 question have to we attempted & 3 from lach part.
There are 3 options
(1)3 from part 1 & % from part 2
no, of ways
=5C3×7C5
=3!(5−3)!5!×5!(7−5)!7!
=25×4×=27×6
=5×2×7×3
=210 ways
(2)4 from part 1 & 4 from part 2
=5C4×7C4
=4!(5−4)!5!×=4!(7−4)!7!
=5×=3×2×17×6×5
=5×7×5
=175 ways
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