Question
If n is the number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any quation find n/40.

2919

2907

2668

None of these
easy
Solution
2907
The maximum masks that can be assigned to any question is 16. If x_{i} are the marks assigned to ith question, then x_{1} + x_{2} + … + x_{8} = 30 and 2 ≤ x_{i}≤ 16 for i = 1, 2, … 8.
Put x_{i} = y_{i} + 2, so that y_{i} ≥ 0 and y_{1} + y_{2} + … + y_{8} = 14.
The number of nonnegative integral solutions of this equations is .
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