Multiple choice

A die is rolled three times, the probability of getting a large number then the previous number is

  1. $\dfrac {5}{216}$
  2. $\dfrac {5}{54}$
  3. $\dfrac {1}{6}$
  4. $\dfrac {5}{36}$
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B Correct answer
Explanation

Total outcomes for 3 dice = 6^3 = 216. We need x1 < x2 < x3. The number of ways to choose 3 distinct numbers from 6 is 6C3 = 20. Since there is only one way to arrange them in increasing order, the probability is 20 / 216 = 5 / 54.

AI explanation

When a die is rolled three times, the total number of possible outcomes is 6 times 6 times 6, which is 216. To get a strictly increasing sequence of three distinct numbers, we must choose any 3 different numbers from the 6 available, which can be done in 6C3 ways. For each chosen set of 3 numbers, there is exactly one way to arrange them in increasing order, giving 20 favorable outcomes, so the probability is 20/216, which simplifies to 5/54.

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