A guardian with 6 wards wishes everyone of them to study either Law or Medicine or Engineering. Number of ways in which he can make up his mind with regard to the education of his wards if every one of them be fit for any of the branches to study, and atleast one child is to be sent in each discipline is :

120

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216

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729

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540

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Solution

The correct option is D 540
6 wards been given in the problem.
Let,
Law= $3 * 3$
Medicine= $3 * 3$
Engineering= $3 * 3$
Total= $3^{6}$
Requirements=Total-(All in two disciplines)-(One in one discipline)
$=729 - {}^3C_2 \quad ( 2^6-2)-3$
$= 729 - 3 \times 62 - 3$
$= 729 - 189$
Answer =540

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The correct option is D 5406 wards been given in the problem.Let,Law=3∗3Medicine=3∗3Engineering=3∗3Total=36Requirements=Total-(All in two disciplines)-(One in one discipline) $=729 - {}^3C_2 \quad ( 2^6-2)-3$ =729−3×62−3 =729−189 Answer =540

The correct option is D 540
6 wards been given in the problem.
Let,
Law= $3 * 3$
Medicine= $3 * 3$
Engineering= $3 * 3$
Total= $3^{6}$
Requirements=Total-(All in two disciplines)-(One in one discipline)
$=729 - {}^3C_2 \quad ( 2^6-2)-3$
$= 729 - 3 \times 62 - 3$
$= 729 - 189$
Answer =540