Mathematics - Permutation & Combination Question with Solution | TestHub

30 marks to be alloted to 8 questions. Each question 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, $a_2\ge 0,\dots \dots .a_8\ge 0$ So, $\begin{array}{c}{a}_1+a_2+\dots \dots +a_8\\ +2+2+\dots ..+2\end{array}\}=30$ $\Rightarrow a_1+a_2+\dots \dots +a_8=30-16=14$ So, this is a problem of distributing 14 articles in 8 groups. Number of ways $={}^{14+8-1}{\mathrm{C}}_{8-1}={}^{21}{\mathrm{C}}_7$