Multiple choice

Three perfect dice D1, D2 and D3 are rolled. Let x, y and z represent the numbers on D1, D2 and D3, respectively. What is the number of possible outcomes such that x < y < z?

  1. 20

  2. 18

  3. 14

  4. 10
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A Correct answer
Explanation

We need to choose 3 distinct numbers from {1, 2, 3, 4, 5, 6} such that x < y < z. This is equivalent to choosing any 3 distinct numbers, as there is only one way to arrange them in increasing order. The number of ways is 6C3 = (6*5*4)/(3*2*1) = 20.

AI explanation

The problem asks for the number of combinations of 3 distinct numbers chosen from 6, since the numbers on the dice must be in strictly increasing order. Using the combinations formula, this is calculated as 6C3. Calculating 6! / (3! * 3!) yields (6 * 5 * 4) / (3 * 2 * 1) = 20 possible outcomes.

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