I would like to have the explanation for the 1st one.
I tried the following:-
1) Total no. of possibilities = 6*6*6 = 216
No. of events where all the three are equal = 6
No. of events when none are eqaul = 6*5*4 = 120
Therefore the no. of events when two are equal and third different
= 216-6-120 = 90
Therefore Probability that 2 are equal and third is different = 90 / 216
The remaining two I got the answers same as 5/18 and 5/324 respectively.
I agree with indiatimes on this one. My method was the same:
All three numbers the same we have 6/216.
All three different we have 120/216.
So the remainder is 90/216, reducing to 5/12.