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.

624

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208

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2304

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None

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Solution

The correct option is A $624$
Total no. of ways
$A$ $B$ $C$ $A$ $B$ $C$
$= (^{4} C_{1} \times^{4} C_{1} \times^{4} C_{3}) \times 3 + (^{4} C_{1}^{4} C_{2}^{4} C_{2}) \times 3$ ( $∴$ multiple by 3 as for each A,B,C different combination)
$= 192 + 432$
$= 624$

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