Question

In paper of English there are 5 questions such that the sum of marks is 30 and the marks
for any question is not less than 2 and not more than 8. If the number of ways in which
marks can be awarded is a 3 digit number xyz then the value of 2  
5
x  y  z is equal to
? (Given that marks can be allotted in integers only)

Answer 1

The problem is same as the no. of positive integral solution of q1+q2+q3+........+q8=30 such that qi≥2∀i∈(1,8)
So let's distribute 2 to each qi , so now the equation becomes q1+q2+q3+........+q8=30−16⇒q1+q2+q3+........+q8=14
Therefore, the no. of non-negative integral solution with constraint =(14+8-1  14) = ( 21  14 )

Hence the number of ways are  ( 21  14 )