What is the probability that when we roll four fair 6-sided dice, they won't all show the same number?

The number of possibilities if all the dice look different is 6^4

Only 6 of those will have every cie the sames

So   P(all the same number )=     $${\frac{{\mathtt{6}}}{{{\mathtt{6}}}^{{\mathtt{4}}}}} = {\frac{{\mathtt{1}}}{{\mathtt{216}}}} = {\mathtt{0.004\: \!629\: \!629\: \!629\: \!629\: \!6}}$$

 

P (they are not all the same)  =   $${\mathtt{1}}{\mathtt{\,-\,}}\left({\frac{{\mathtt{6}}}{{{\mathtt{6}}}^{{\mathtt{4}}}}}\right) = {\frac{{\mathtt{215}}}{{\mathtt{216}}}} = {\mathtt{0.995\: \!370\: \!370\: \!370\: \!370\: \!4}}$$

I am almost positive that I saw this exact question already answered today.

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