GATE CS 2024 Set 2 Q.18: Probability and Statistics

When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers (i.e., 1, 2, 3, 4, 5, and 6) is

$\frac{1}{324}$

$\frac{5}{324}$

$\frac{7}{324}$

$\frac{11}{324}$

Official answer and solution

Solution

Divide the number of favorable outcomes ( $6!$ ) by the total number of outcomes ( $6^6$ ).

When $6$ unbiased six-sided dice are rolled simultaneously:

Therefore, the required probability is:

P = \frac{6!}{6^6} = \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{6^6} = \frac{120}{6^4} = \frac{20}{216} = \frac{5}{324}

Final answer

Option (B)

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

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