When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers is

A. 1/6
B. 5/324
C....

Question

When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers is

A. 1/6
B. 5/324
C. 1/54
D. 5/1296

Accepted Answer

P(all distinct) = 5/324   [Option B] Six dice are rolled and we want all six to show different numbers (i.e., each of 1, 2, 3, 4, 5, 6 exactly once). The total number of outcomes is 6^6. The number of outcomes where all six numbers are distinct is 6! (arrange 1-6 among the 6 dice). The probability is 6! / 6^6 = 720 / 46656 = 5/324.

When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers is A. 1/6 B. 5/324 C. 1/54 D. 5/1296