Question

Q.4
If three dice are rolled simultaneously, then what is the probability that the sum of the numbers appearing on the top face of the dice is 12 ?
a)25/216
b)2/27
c)11/108
d)1/36

Answer 1

its not the most elegant solution, but you could list out all the combinations of numbers between 1-6 that sum to 12, then think of those combinations and see how many ways they could be made with the 3 dice. finally divide by 6^3 or 216
so just going through it...

1-5-6 (6 ways)
2-4-6 (6 ways)
2-5-5 (3 ways)
3-3-6 (can be made 3 different ways with the dice)
3-4-5 (6 ways)
4-4-4 (1 way)

unless i've missed any, that results in 6+6+3+3+6+1 = 25 ways to make 12 out of 216 possible rolls

Answer 2

ohh yes u r right i was taking 1-5-6 as to be in 3 ways, my bad. Thanks a lot :)

Answer 3

no worries!
As i'm sure you know, any time there are 3 different numbers, it can be written 6 ways (eg 123, 132, 213, 231, 312, 321)
if there are 2 different numbers its only 3 (eg 122, 212, 221)
and if all three are a single number it can only happen once