Q119 / 120 · NDA 2024 (Phase 2) · Mathematics

Three perfect dice $\mathrm{D}_1, \mathrm{D}_2$ and $\mathrm{D}_3$ are rolled. Let $x, y$ and $z$ represent the numbers on $\mathrm{D}_1, \mathrm{D}_2$ and $\mathrm{D}_3$ respectively. What is the number of possible outcomes such that $x < y < z$ ?

  • Correct answer
    A
    20
  • B
    18
  • C
    14
  • D
    10

Solution

Let $x, y, z$ are represent the numbers on three dice possible outcomes such that $\mathrm{n} < \mathrm{y} < \mathrm{z}$ $\begin{aligned} & =(1,2,3)(1,2,4),(1,2,5),(1,2,6),(1,3,4),(1,3,5) \\ & (1,3,6),(1,4,5),(1,4,6),(1,5,6),(2,3,4),(2,3,5),(2, \\ & 3,6),(2,4,5),(2,4,6),(2,5,6),(3,4,5),(3,4,6),(3,5, \\ & 6),(4,5,6) \\ & \therefore \quad \text { Total possible outcomes }=20 \end{aligned}$

Hence, the correct answer is option: 'A'.

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