# You roll a number cube 4 times. What is the probability that you roll a 6,5,4,and a 3?

Apr 5, 2016

$\frac{1}{54}$
First, let's count the ways we can roll $6 , 5 , 4 ,$ and $3$. There are four possibilities for our first roll. After that, there are three possibilities for our second roll (as one of the numbers has been rolled already). Then there are two possibilities for our third roll, and our last roll has only one possibility. Thus, there are $4 \cdot 3 \cdot 2 \cdot 1 = 24$ ways to roll those four specific numbers.
Now, let's count the total possible rolls we could have. There are six possibilities for the first roll, six for the second roll, six for the third roll, and six for the fourth roll. Therefore there are $6 \cdot 6 \cdot 6 \cdot 6 = 1296$ possible rolls.
Putting these together, we have the probability of rolling $6 , 5 , 4 ,$ and $3$ as $\frac{24}{1296} = \frac{1}{54}$