Question

What is the number of ways in which an examiner can assign 10 marks to 4 questions, giving not less than 2 marks to any questions?
(A) 4
(B) 6
(C) 10
(D) 16

Answer 1

Ans: (C)
Hint : $x_{1}+x_{2}+x_{3}+x_{4}=10 \quad x_{i} \geq 2$
$$\Rightarrow\left(x_{1}-2\right)+\left(x_{2}-2\right)+\left(x_{3}-2\right)+\left(x_{4}-2\right)=2$$

$$\begin{aligned} &y_{1} \quad y_{2} \quad y_{3} \quad y_{4} \\ &y_{1}+y_{2}+y_{3}+y_{4}=2 ; \quad y_{i} \geq 0 \\ &\therefore \text { N.O.W }={ }^{2+4-1} c_{4-1}={ }^{5} c_{3}=10 \end{aligned}$$

Answer 2

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