Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2024 · Mathematics · Permutation and Combination

Three perfect dice D_1, D_2 and D_3 are rolled. Let x, y and z...

Three perfect dice D1,D2\mathrm{D}_1, \mathrm{D}_2 and D3\mathrm{D}_3 are rolled. Let x,yx, y and zz represent the numbers on D1,D2\mathrm{D}_1, \mathrm{D}_2 and D3\mathrm{D}_3 respectively. What is the number of possible outcomes such that x<y<zx < y < z ?

Options

  1. A20
  2. B18
  3. C14
  4. D10

Correct answer

A. 20

Step-by-step solution

Let x,y,zx, y, z are represent the numbers on three dice possible outcomes such that n<y<z\mathrm{n} < \mathrm{y} < \mathrm{z}=(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)∴ Total possible outcomes =20\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}$$
Practice Permutation and Combination on Quantrex Academy →

More from Permutation and Combination

All Permutation and Combination questions Full Permutation and Combination list Permutation and Combination JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs