Six dice are thrown simultaneously. The probability that all of them show the different faces, is

Options

A. `(1)/(6^(5))`
B. `(6!)/(6^(6))`
C. `(1)/(6!)`
D. `(5!)/(6!)`

Answer

B

Explanation

The total number of ways in which all dice show different faces is same as the number of arrangements of 6 numbers 1,2,3,4,5,6 by taking all at a time.
So, favourable number of elementary events -6 !
Hence, required probaility `=(6!)/(6^(6))`