Thread: 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:


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.

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:

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.

I get one-half your answer.
The string can be arranged in ways.
We can have six times that number to account for the fact each of the six sides can be doubled.
There are a total of possible strings,

Thanks, Plato! You're right! The division of 2! to remove the repeated number during the 7th throw. Thanks!!