# Finding the probability of 7 Trials, All 6 success

• Mar 13th 2012, 09:21 AM
xEnOn
Finding the probability of 7 Trials, All 6 success
Suppose I roll a fair dice for 7 times. What is the probability that I will roll all the 6 sides of the dice?

What I have done is this:
$\left ( \frac{1}{6} \right )^6\times 7! = \frac{35}{324}$

But is this correct?

I am not sure if the above is correct because I thought it could be a Negative Binomial distribution too. The 7 throws with 6 sides show up is somewhat daunting and makes the question confusing.
• Mar 13th 2012, 09:48 AM
Plato
Re: Finding the probability of 7 Trials, All 6 success
Quote:

Originally Posted by xEnOn
Suppose I roll a fair dice for 7 times. What is the probability that I will roll all the 6 sides of the dice?
What I have done is this:
$\left ( \frac{1}{6} \right )^6\times 7! = \frac{35}{324}$
But is this correct? I am not sure if the above is correct because I thought it could be a Negative Binomial distribution too. The 7 throws with 6 sides show up is somewhat daunting and makes the question confusing.

The string $1123456$ can be arranged in $\frac{7!}{2!}$ ways.
There are a total of $6^7$ possible strings,