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Standard XII

Mathematics

Permutation: n Different Things Taken All at a Time When All Are Not Different.

A question pa...

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.

624

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208

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2304

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N o n e

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Solution

The correct option is A $624$
Five questions can be answered in the following way

$A$ $B$ $C$
$1$ $1$ $3$ $4 C_{1} \times 4 C_{1} \times 4 C_{3}$ $64$
$1$ $2$ $2$ $4 C_{1} \times 4 C_{1} \times 4 C_{3}$ $144$
$2$ $2$ $1$ $4 C_{1} \times 4 C_{1} \times 4 C_{3}$ $144$
$2$ $1$ $2$ $4 C_{1} \times 4 C_{1} \times 4 C_{3}$ $144$
$3$ $1$ $1$ $4 C_{1} \times 4 C_{1} \times 4 C_{3}$ $64$
$1$ $3$ $1$ $4 C_{1} \times 4 C_{1} \times 4 C_{3}$ $64$
Therefore total number of ways $= 64 + 144 + 144 + 144 + 64 + 64 = 624$

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$A$	$B$	$C$
$1$	$1$	$3$	$4 C_{1} \times 4 C_{1} \times 4 C_{3}$	$64$
$1$	$2$	$2$	$4 C_{1} \times 4 C_{1} \times 4 C_{3}$	$144$
$2$	$2$	$1$	$4 C_{1} \times 4 C_{1} \times 4 C_{3}$	$144$
$2$	$1$	$2$	$4 C_{1} \times 4 C_{1} \times 4 C_{3}$	$144$
$3$	$1$	$1$	$4 C_{1} \times 4 C_{1} \times 4 C_{3}$	$64$
$1$	$3$	$1$	$4 C_{1} \times 4 C_{1} \times 4 C_{3}$	$64$

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.

The correct option is A 624Five questions can be answered in the following way ABC 113 4C1×4C1×4C3 64 12 2 4C1×4C1×4C3 144 221 4C1×4C1×4C3 144 2 1 2 4C1×4C1×4C3 144 3 1 1 4C1×4C1×4C3 64 1 3 1 4C1×4C1×4C3 64Therefore total number of ways =64+144+144+144+64+64=624

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