Let ω be a complex cube root of unity with ω≠1. A fair die is thrown three times. If r1,r2 and r3 are the
numbers obtained on the die, then the probability that ωr1+ωr2+ωr3=0 is
118
19
29
136
r1,r2,r3∈{1,2,3,4,5,6}
r1,r2,r3 are of the form 3k,3k+1,3k+2
Required probability =3!×2C1×2C1×2C16×6×6=6×8216=29