The number of ways in which a score of 11 can be made from a throw by three persons,each throwing a single die once, is

Options

A. 45
B. 18
C. 27
D. 68

Answer

C

Explanation

Coefficient of `x^(11)` in `(x+x^(2)+x^(3)+x^(4)+x^(5)+x^(6))^(3)`
=Coefficient of `x^(8)` in
`(1+x+x^(2)+x^(3)+x^(4)+x^(5))^(3)`
=Coefficient of `x^(8)` in `(1-x^(6))^(3)(1-x)^(-3)`
=Coefficient of `x^(8)` in `(1-3x^(6))(1+.^(3)C_(1)x+ . . )`
`=.^(10)C_(2)-3xx.^(4)C_(2)=45-18=27`