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 \lt y \lt z?

Explanation

The dice can show values from 1 to 6. For the condition x \lt y \lt z to hold, we need to choose any 3 distinct numbers from the set \{1, 2, 3, 4, 5, 6\}. Once chosen, there is exactly one way to arrange them in strictly increasing order. The number of ways to select 3 distinct numbers from 6 is \binom{6}{3} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20.

Related questions on Algebra

• How many four-digit natural numbers are there such that <strong>ALL</strong> of the digits are odd?
• What is \sum_{r=0}^{n}2^{r}C(n,r) equal to ?
• If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with or without meaning) a...
• Consider the following statements : 1. If f is the subset of Z\times Z defined by f=\{(xy,x-y);x,y\in Z\}, then f is a function from...
• For how many quadratic equations, the sum of roots is equal to the product of roots?