Thread: Finding the probability of 7 Trials, All 6 success

1. 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:
$\displaystyle \left ( \frac{1}{6} \right )^6\times 7! = \frac{35}{324}$

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.

2. Re: Finding the probability of 7 Trials, All 6 success 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:
$\displaystyle \left ( \frac{1}{6} \right )^6\times 7! = \frac{35}{324}$
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 $\displaystyle 1123456$ can be arranged in $\displaystyle \frac{7!}{2!}$ ways.
There are a total of $\displaystyle 6^7$ possible strings,
Thanks, Plato! You're right! The division of 2! to remove the repeated number during the 7th throw. Thanks!! finding, probability, success, trials 