# The Probability of Rolling a Large Straight with 5 Six-Sided Dice [duplicate]

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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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## marked as duplicate by Ross Millikan, vadim123, T. Bongers, Dominic Michaelis, Bruno JoyalNov 26 '13 at 5:23

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

What have you tried? Where are you getting stuck? –  Matthew Conroy Nov 26 '13 at 4:33
Matthew Conroy, it's about getting different consecutive numbers on every die in different ways –  user111236 Nov 26 '13 at 4:53
But now I know! It's a 48 in 7,776 chance of rolling a large straight. –  user111236 Nov 26 '13 at 15:04
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? –  user111236 Nov 27 '13 at 15:06

## 1 Answer

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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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! –  user111236 Nov 26 '13 at 15:01
You're welcome, glad to be of service. –  vadim123 Nov 26 '13 at 15:14
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?! –  user111236 Nov 26 '13 at 16:24