Discrete Math- Four different dice are rolled

Question

Four different dice are rolled. a) In how many outcomes will at least one five appear? b) In how many outcomes will the highest die be a five?

I think i figured out the answer for how many outcomes will the five appear at least once. So what I got was that there are total of 6^4 of total outcomes which is 1296 - 5^4 = 671 outcomes for at least on five to appear. (correct me if im wrong). Though I have no idea how to approach question b)? Does anyone know how to do this?

Part (a) looks good. The highest die being a five is the same thing as saying you rolled at least one five and you rolled no sixes. — John Habert, Jan 30 '14 at 03:23
if I coun't that I rolled no sixes, that wouldn't make sense because the highest number can be a different number too? highest die can be a 4? or a 3? or a 2? — Roy Kesserwani, Jan 30 '14 at 03:24

André Nicolas · Answer 1 · 2014-01-30T03:31:49.817

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Hint: All rolls are $\le 5$ and it is not true that all rolls are $\le 4$.

(We interpreted "the highest is $5$" to mean one or more $5$'s occur, but nothing higher.)

edited Jan 30 '14 at 03:31

answered Jan 30 '14 at 03:25

André Nicolas

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so I would approach it by considering that I rolled no sixes, right? – Roy Kesserwani Jan 30 '14 at 03:28
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The hint leads directly to the answer $5^4-4^4$. Forget about $6$'s (though you could do it that way too). – André Nicolas Jan 30 '14 at 03:29
The answer for part b is $5^{4} - 4^{4}$? I am having a bit of trouble understanding why. Does $5^{4}$ mean rolls with only 1-5, excluding 6? – Zaku Mar 18 '19 at 08:10

Discrete Math- Four different dice are rolled

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