A) \[^{30}{{C}_{7}}\]
B) \[^{21}{{C}_{8}}\]
C) \[^{21}{{C}_{7}}\]
D) \[^{30}{{C}_{8}}\]
Correct Answer: C
Solution :
30 marks to be alloted to 8 questions. Each question has to be given \[\ge 2\] marks Let questions be \[a,\text{ }b,\text{ }c,\text{ }d,\text{ }e,\text{ }f,\text{ }g,\text{ }h\] and \[a\text{ }+\text{ }b\text{ }+\text{ }c\text{ }+\text{ }d\text{ }+\text{ }e\text{ }+f+\text{ }g\text{ }+\text{ }h\text{ }=\text{ }30\] Let a \[a={{a}_{1}}+2\] so, \[{{a}_{1}}\ge 0\] \[b={{a}_{2}}+2\]so, \[{{a}_{2}}\ge 0,......,{{a}_{g}}\ge 0\] 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 \[={{\,}^{14+8-1}}{{C}_{8-1}}={{\,}^{21}}{{C}_{7}}\]
You need to login to perform this action.
You will be redirected in
3 sec
