Multiple choice

If five dices are tossed, then what is the probability that the five numbers shown will be different?

  1. $\dfrac {5}{54}$
  2. $\dfrac {5}{18}$
  3. $\dfrac {5}{27}$
  4. $\dfrac {5}{81}$
  5. $\dfrac {5}{36}$
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A Correct answer
Explanation

Total outcomes = 6^5. Favorable outcomes (all different) = 6 * 5 * 4 * 3 * 2 = 720. Probability = 720 / 7776 = 5 / 54.

AI explanation

The total number of outcomes for rolling five dice is 6^5, which equals 7776. The number of ways to get five different numbers is found using permutations, calculated as 6P5, which equals 720. The probability is 720 divided by 7776. By simplifying the fraction, the result is 5/54.

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