If I have 6 regular dice, (each numbered 1-6):
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What is the probability that when rolled that each will be a different number.(each individual di is a different number from 1-6, but a random order)
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What is the probability that of the six rolls, each will be an increasing number starting with 1. (First roll is 1, second is 2, etc.)
I came up with this problem after watching an episode of numberphile. Thanks!
Best Answer
There are $6^6$ ways of throwing the dice in total. There are $6!$ ways of throwing all the numbers from 1 to 6 in any order. There is only one way of throwing $1,2,3,4,5,6$.
Hence your first answer is $6!/6^6$, and your second is $1/6^6$.