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

• Aug 27th 2012, 07:18 PM
Cindz83
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 :(
• Aug 27th 2012, 07:49 PM
MaxJasper
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%
• Aug 27th 2012, 08:32 PM
Soroban
Re: Six dice are rolled at one time. What's the probability that all six faces differ
Hello, Cindz83!

Quote:

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. = $\tfrac{6}{6}$

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

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

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

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

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

Therefore: . $P(\text{6 different numbers}) \:=\:\frac{6}{6}\cdot\frac{5}{6}\cdot\frac{4}{6} \cdot \frac{3}{6}\cdot \frac{2}{6}\cdot\frac{1}{6} \:=\:\frac{5}{324}$
• Aug 28th 2012, 07:21 AM
bizworldusa
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
• Aug 28th 2012, 08:24 AM
Wilmer
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...