I don't know the probability of rolling a large straight with 5 six-sided dice, so I need to know what the probability is. What is it?
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$\begingroup$ Matthew Conroy, it's about getting different consecutive numbers on every die in different ways $\endgroup$– user111236Nov 26, 2013 at 4:53
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$\begingroup$ But now I know! It's a 48 in 7,776 chance of rolling a large straight. $\endgroup$– user111236Nov 26, 2013 at 15:04
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$\begingroup$ I hope this answer is right, you know, the probability comment that's above this one that I answered yesterday (Tuesday, November 26, 2013). Also, why should comments typed in by yourself be edited up to 5 minutes? $\endgroup$– user111236Nov 27, 2013 at 15:06
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1 Answer
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The probability of rolling 1-2-3-4-5 in that order is $(1/6)^5$. However any order will do, so it's $5!(1/6)^5$.
The probability of rolling 2-3-4-5-6 is similarly $5!(1/6)^5$.
Combining, we get $240(1/6)^5\approx 0.03$, i.e. about 3% of the time.
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$\begingroup$ Wow! That's amazing! Awesome! Fantastic! I can't believe you used a factorial and an exponent to figure that out! You also used a similarity thing! Another thing you used is an "approximately equal to" sign to approximate the answer. No doubt about it! $\endgroup$ Nov 26, 2013 at 15:01
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$\begingroup$ But I didn't even say "Thank you." and how are you out of service? Also, how can you be glad when you're out of service?! $\endgroup$ Nov 26, 2013 at 16:24