If I have 6 regular dice, (each numbered 1-6):
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)
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!