Q.

The number of ordered triplets of positive integers which are solutions of the equation x + y + z = 100 is

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a

5081

b

6005

c

4851

d

None of these

answer is C.

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Detailed Solution

The number of triplets of positive integers which are solutions of x + y + z = 100= Coefficient of x100 in x+x2+x3+…3= Coefficient of x100 in x3(1−x)−3= Coefficient of x100 in x31+3x+6x2+…+(n+1)(n+2)2xn+…=(97+1)(97+2)2=49×99=4851
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The number of ordered triplets of positive integers which are solutions of the equation x + y + z = 100 is