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

Options

A. 45
B. 18
C. 27
D. none of these

Answer

C

Explanation

Required number of ways
= Coeff. of `x^(11)" in "(x+x^(2)+......+x^(6))^(3)`
= Coeff. of `x^(8)" in "(1+x+x^(2)+......+x^(5))^(3)`
= Coeff. of `x^(8)" in "((1-x^(6))/(1-x))^(3)`
Coeff. of `x^(8)" in "(1-x^(6))^(3)(1-x)^(-3)`
= Coeff. of `x^(8)" in "(1-""^(3)C_(1)x^(6)+....)(1-x)^(-3)`
= Coeff. of `x^(8)" in "(1-x)^(-3)-""^(3)C_(1)."Coff. of "x^(2)" in "(1-x)^(-3)`
`=""^(8+3-1)C_(3-1)-""^(3)C_(1).""^(2+3-1)C_(3-1)=""^(10)C_(2)-3xx""^(4)C_(2)=27`