Dice probability

**chengbin** · Sep 10th 2009, 05:45 PM

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.

**Grandad** · Sep 10th 2009, 11:19 PM

Hello chengbin

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.