Multiple choice

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

  1. $\cfrac{1}{{6}^{5}}$
  2. $\cfrac{6!}{{6}^{6}}$
  3. $\cfrac{1}{{6!}^{}}$
  4. $\cfrac{5!}{{6}^{6}}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total outcomes for 6 dice is 6^6. Favorable outcomes where all show different faces is the number of permutations of 6 distinct items, which is 6!. Probability = 6! / 6^6.

AI explanation

The total number of outcomes when six dice are thrown is 6^6. For all dice to show different faces, the outcomes must be a permutation of the numbers 1 through 6, giving 6! favorable outcomes. Using the classical definition of probability, the probability is the ratio of favorable outcomes to total outcomes, which is 6! divided by 6^6.

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