Question

A question paper is divided into two parts $$A$$ and $$B$$ and each part contains $$5$$ questions. The number of ways in which a candidate can answer $$6$$ questions selecting at least two questions from each part is:

A
80
B
100
C
200
D
None of these

Solution

The correct option is C $$200$$ $$(A)$$ $$(B)$$  $$(5\, question)$$$$(5\, question)$$  $$(i)$$$$2$$$$4$$$$=6$$$$(ii)$$$$3$$$$3$$$$=6$$$$( iii)$$$$4$$$$2$$$$=6$$There are two section and the candidates has to answer at least $$2$$ question from each section with total of $$6$$ questions.So, there are three followign ways.$$(i)$$ no of ways $$\Rightarrow$$ selecting $$2$$ questions from section $$A$$ and $$4$$ questions from sections $$B$$$$\Rightarrow ^5C_2\times ^5C_4 \Rightarrow 10\times 5 \Rightarrow 50$$$$(ii)$$ no. of ways $$\Rightarrow$$ selecting $$3$$ questions from each section.$$\Rightarrow ^5C_3\times ^5C_3\Rightarrow 10\times 19=100$$$$(iii)$$ no. of ways $$\Rightarrow$$ selecting $$4$$ from section $$A$$ and $$2$$ from section $$B$$ $$\Rightarrow ^5C_4\times ^5C_2\Rightarrow 5 \times 10\Rightarrow 50$$$$\therefore$$ Total no. of ways $$=50+100+50=200$$. Maths

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