Question

# A question paper on mathematics consists of twelve questions divided into three parts $$A,B$$ and $$C$$ each containing four questions. In how many ways can an examinee answer five questions, selecting atleast one from each part.

A
624
B
208
C
2304
D
None

Solution

## The correct option is A $$624$$Five questions can be answered in the following way $$A$$$$B$$$$C$$   $$1$$$$1$$$$3$$ $$4C_1 \times 4C_1 \times 4C_3$$ $$64$$ $$1$$$$2$$ $$2$$  $$4C_1 \times 4C_1 \times 4C_3$$ $$144$$ $$2$$$$2$$$$1$$ $$4C_1 \times 4C_1 \times 4C_3$$  $$144$$ $$2$$ $$1$$ $$2$$ $$4C_1 \times 4C_1 \times 4C_3$$ $$144$$ $$3$$ $$1$$ $$1$$ $$4C_1 \times 4C_1 \times 4C_3$$ $$64$$ $$1$$ $$3$$ $$1$$ $$4C_1 \times 4C_1 \times 4C_3$$ $$64$$Therefore total number of ways $$=64+144+144+144+64+64=624$$Maths

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