A question paper has two sections. section I has 5 questions and section II has 6 questions. A student must answer at least two questions from each section among 6 questions he answers. How many different choices does the student have in choosing questions?
Solution
A question paper has two sections.
Number of questions in section I = 5
Number of questions in section II = 6
At least 2 questions have to be selected from each section and all 6 questions are to be selected.
This can be done as follows:
(I) 2 questions (out of 5) from section I and
4 questions (out of 6) from section II are selected.
or (II) 3 questions from section I and
3 questions from section II are selected.
or (III) 4 questions from section I and
2 questions from section II are selected.
Now, number of selections in (I)
=`""^5"C"_2 xx ""^6"C"_2`
= `(5 xx 4)/(2 xx 1) xx (6 xx 5)/(2 xx 1)`
= 10 × 15
= 150
Number of selections in (II)
= =`""^5"C"_3 xx ""^6"C"_3`
= `(5 xx 4)/(2 xx 1) xx (6 xx 5 xx)/(3 xx 2 xx 1)`
= 10 × 20
= 200
Number of selections in (III)
= =`""^5"C"_4 xx ""^6"C"_2`
= `5 xx (6 xx 5)/(2 xx 1)`
= 75
By addition principle, total number of required selections
= 150 + 200 + 75
= 425
