In how many ways can 30 marks be allotted to 8 question if each question carries at least 2 marks?

Answer

`.^(21)C_(14)`

Explanation

Required number
`="coeff. Of" p^(30) " in" (p^(2)+p^(3)+..+ p^(16))^(8)`
`= "coeff.of" p^(30) "in" p(16)(1+p+..+ p^(14))^(8)`
`="coeff.of" p^(14) " in" ((1-p^(15))/(1-p))^(8)`
`="coeff.of" p^(14) " in" (1-p)^(-8)`
`=.^(21)C_(14)`