Q.

The number of ways in which 30 marks can be alloted to 8 questions if each question carries at least 2 marks, is

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a

115280

b

117280

c

116280

d

None of these

answer is C.

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Detailed Solution

Required number = coefficient of x30 in (x2 + x3 + … + x16)8                           = coefficient of x30 in x161+x+…+x148= coefficient of x14 in 1−x151−x8= coefficient of x14 in (1−x)−8=21C14=116280
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The number of ways in which 30 marks can be alloted to 8 questions if each question carries at least 2 marks, is