# Thread: Six dice are rolled at one time. What's the probability that all six faces differ?

1. ## Six dice are rolled at one time. What's the probability that all six faces differ?

show work? I don't understand how to do this, no one taught me a formula

2. ## Re: Six dice are rolled at one time. What's the probability that all six faces differ

{1,2,3,4,5,6} = 6
{1,2,3,4,5}=5
4
3
2
1
Prob(all faces different)=1*2*3*4*5*6/6^6 = .015432 = 1.5432%

3. ## Re: Six dice are rolled at one time. What's the probability that all six faces differ

Hello, Cindz83!

Six dice are rolled at one time.
What is the probability that all six dice shows different numbers?

They taught you "the formula".
You just don't know how to apply it.

The first die can be any number: Prob. = $\displaystyle \tfrac{6}{6}$

The second die must not match the first die: Prob. = $\displaystyle \tfrac{5}{6}$

The third die must not match the first 2 dice: Prob. = $\displaystyle \tfrac{4}{6}$

The fourth die must not match the first 3 dice: Prob. = $\displaystyle \tfrac{3}{6}$

The fifth die must not match the first 4 dice: Prob. = $\displaystyle \tfrac{2}{6}$

The sixth die must not match the first 5 dice: Prob. - $\displaystyle \tfrac{1}{6}$

Therefore: .$\displaystyle P(\text{6 different numbers}) \:=\:\frac{6}{6}\cdot\frac{5}{6}\cdot\frac{4}{6} \cdot \frac{3}{6}\cdot \frac{2}{6}\cdot\frac{1}{6} \:=\:\frac{5}{324}$

4. ## Re: Six dice are rolled at one time. What's the probability that all six faces differ

I am completely agree with the SOROBON.
Thank you for providing this
Bizworldusa

5. ## Re: Six dice are rolled at one time. What's the probability that all six faces differ

cobooboc and bizworldusa: get lost !!
All you want to do is advertize, not help...