Answer: Option A
The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
$$\eqalign{
& = 6 \times 6 \times 6 \times 6 = {6^4} \cr
& n(S) = {6^4} \cr} $$
Let X be the event that all dice show the same face.
X = {(1, 1, 1, 1), (2, 2, 2, 2), (3, 3, 3, 3), (4, 4, 4, 4), (5, 5, 5, 5), (6, 6, 6, 6)}
n(X) = 6
Hence required probability,
$$\eqalign{
& = \frac{{n(X)}}{{n(S)}} = \frac{6}{{{6^4}}} \cr
& = \frac{1}{{216}} \cr} $$