A) \[^{30}{{C}_{7}}\]
B) \[^{21}{{C}_{8}}\]
C) \[^{21}{{C}_{7}}\]
D) \[^{30}{{C}_{8}}\]
Correct Answer: C
Solution :
[c] 30 marks to be allotted to 8 questions. Each questions has to be given \[\ge 2\,\,marks\] Let questions be a, b, c, d, e, f, g, h and \[a+b+c+d+e+f+g+h=30\] Let \[a={{a}_{1}}+2\] so, \[{{a}_{1}}\ge 0,\] \[b={{a}_{2}}+2\,\,\,so,\,\,{{a}_{2}}\ge 0,....{{a}_{8}}\ge 0\] So, \[\left. \begin{matrix} {{a}_{1}}+{{a}_{2}}+...+{{a}_{8}} \\ +2+2+....+2 \\ \end{matrix} \right\}=30\] \[\Rightarrow \,\,\,\,{{a}_{1}}+{{a}_{2}}+...+{{a}_{8}}=30-16=14\] So, this is a problem of distributing 14 articles in 8 groups. Number of ways \[{{=}^{14+8-1}}{{C}_{8-1}}{{=}^{21}}{{C}_{7}}\]
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