Question

In how many ways in which an examiner can assign $30$ marks to $8$ questions giving not less than $2$ marks to any question ?

• A. ${}^{21}{C}_7$
• B. ${}^{22}{C}_7$
• C. ${}^{23}{C}_7$
• D. None of the above

Answer 1

The correct option is A ${}^{21}{C}_7$

$x_1+x_2+x_3.....+x_8=30$

$x_i\ge 2$

$x_i-2=y_i$

$y_i\ge 0$

$\Rightarrow y_1+y_2+y_3.....+y_8=30$

Number of solutions are ${}_{}^{n+r-1}{C_{r-1}=}^{21}{C}_7$