Correct Answer - A
The total number of elementary events associated with the experiment of throwing four dice is 6×6×6×6=64.
Favourable number of elementary events
= Coefficient of x13 in (x1+x2+x3+x4+x5+x6)4
= Coefficient of x9 in (1+x+x2+..+x5)4
= Coefficient of x9 in (
1-x6
1-x
)4
= Coefficient of x9 in (1-x6)4(1-x)-4
=Coefficient of x9 in (1-.4C1x6+.4C2x12)(1-x)-4
= Coefficient of x9 in (1-x)-4-.4C1× Coefficient of x3 in (1-x)-4
=.9+4-1C4-1-.4C1×.3+4-1C4-1
[∵ Coeff. of xn in(1-x)-r=.n+r-1Cr-1]
=.12C3-4×.6C3=140
∴ Required probability =
140
64
=
35
324
