Multiple choice

Six symmetrical dice are thrown simultaneously. The probability of having different points on them is

  1. $\displaystyle \frac{1}{6}$
  2. $\displaystyle \frac{1}{36}$
  3. $\displaystyle \frac {6!}{6^6}$
  4. $\displaystyle \frac{1}{18}$
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C Correct answer
Explanation

The total number of outcomes when throwing 6 dice is 6^6. The number of ways to have different points on all six dice is the number of permutations of 6 distinct values, which is 6!. Thus, the probability is 6! / 6^6.

AI explanation

The total number of outcomes for rolling six dice is 6^6. To get different points on all six dice, the favorable outcomes are the permutations of the six distinct numbers (1 through 6), which equals 6 factorial. Using the classical probability formula, the required probability is 6 factorial divided by 6^6.

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