Answer:
Step-by-step explanation:
You can do this step by step.
First roll can be any and you can still get the correct outcome.
Second roll has to be different from the first one, that is 5/6
3rd roll will have to be different from the last two, that is 4/6
And so on.
Thus P=1*5/6*4/6*3/6*2/6*1/6, you can simplify this if you wish.
So three consecutive integers 2k,2(k+1),2(k+2)
there sum will be
2k+2(k+1)+2(k+2)
2k+2k+2+2k+4
6k+6
so setting the inequality
102<6k+6<116
subtracting 6 from all sides
96<6k<110
16<k<18.3333
since k is an integer
the only integers between 16 and 18.3
are 17 and 18
so
when k=17
2(17),2(17+1),2(17+2)
34,36,38
when k=18
2(18),2(18+1),2(18+2)
36,38,40
so to check are soultion we substitute
34+36+38=108 which is between 102 and 116
36+38+40=114 which is between 102 and 116
so our soultion is correct
the final answer will be
{{36,38,40},{38,40,42}}