# Dice probability

• Sep 10th 2009, 06:45 PM
chengbin
Dice probability
Given 3 dices are rolled, what is the probability of the sum of the faces is 6?

If n(A) is the number of elementary events in A

$n(A)=_3C_1+_3P_3+_3C_0$

How do you get that?

P.S. How do I properly type permutations in latex? The first number is a bit far to the letter.
• Sep 11th 2009, 12:19 AM
Hello chengbin
Quote:

Originally Posted by chengbin
Given 3 dices are rolled, what is the probability of the sum of the faces is 6?

If n(A) is the number of elementary events in A

$n(A)=_3C_1+_3P_3+_3C_0$

How do you get that?

P.S. How do I properly type permutations in latex? The first number is a bit far to the letter.

The possible scores are:

• one 4 and two 1's. The number of ways of choosing which of the three dice shows the 4 is $^3C_1$.
• one 3, one 2 and one 1. The three dice can be arranged to show these scores in $^3P_3$ ways.
• three 2's. There is no choice involved; all the dice must show the same number. This can be done in $^3C_0$ (or $^3C_3$) ways.

Thus $n(A) = {^3C_1}+{^3P_3} +{^3C_0}$.

LaTeX answer: enclose ^3C_1 in {...}