The number of ways in which an examiner can assign 30 marks to 8 questions, giving not les…

Question

The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question, is:

Accepted Answer

Let each question get $a_i\ge2$, $\sum_{i=1}^8 a_i=30$. Substituting $a_i=b_i+2$: $\sum b_i = 30-16=14$, $b_i\ge0$.

$$\binom{14+8-1}{8-1} = \binom{21}{7}$$

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