Question

The number of ways in which an examiner can assign $30$ marks to $8$ questions, giving not less than $2$ makes to any question is

• A. ${}^{21}{C}_7$
• B. ${}^{21}{C}_8$
• C. ${}^{30}{C}_7$
• D. ${}^{30}{C}_8$

Answer 1

Answer: (A)

${}^{21}{C}_7$

To find the number of ways in which an examiner can assign $30$ marks to $8$ questions giving not less than $2$ makes to any question is:
When $2$ marks assign to each Question, then total number of Questions
$Q_1+Q_2+Q_3+Q_4+Q_5+Q_6+Q_7+Q_8$
$=30-16$
$=14$
Now, Number of non - negative integral solutions can be find out as
$=$ $(\frac{14+8-1}{8-1})$
$=$ $(\frac{21}{7})$
Hence , Option A