Question

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

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

Answer 1

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

After assigning $2$ marks to every question, total $14$ marks are left. Now, distributing $14$ marks to $8$ question.
Using begger's method, the required number of ways
$={}^{14+8-1}{C}_{8-1}={21}_{C_7}$