NDA 2 2024 Maths, question 119

Topic: Probability

Q119

Three perfect dice $D_{1},D_{2}$ and $D_{3}$ are rolled. Let $x,y$ and $z$ represent the numbers on $D_{1},D_{2}$ and $D_{3}$ respectively. What is the number of possible outcomes such that $x<y<z$ ?

(a) $20$ Correct answer
(b) $18$
(c) $14$
(d) $10$

Solution.

Answer: (a) $20$

Choose any three distinct values from 1,…,6.
Each such set has exactly one ordering satisfying x<y<z.
Hence there are C(6,3)=20 outcomes; multiplying by 3! would count forbidden orderings.