- #1
Mandelbroth
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Homework Statement
A friend proposed this question to me. It looks like a homework problem, though, so I'll put it here to avoid any conflict with forum rules.
Suppose you roll a fair 9 sided die (with sides 1 through 9) 4 times. Let A be the value of the first roll, B be the value of the second roll, C be the value of the third roll, and D be the value of the fourth roll.
Find the probability that [itex]A\leq B\leq C\leq D[/itex]
The Attempt at a Solution
I figure that the probability that [itex]A\leq B[/itex] is [itex]\frac{9+36}{81}=\frac{45}{81}[/itex] because there are 9 ways that they can be equal and half of the remaining 72 outcomes have A less than B. However, I'm having difficulty extending this to greater numbers of rolls.
Can someone please help guide me toward my next step? Thank you, in advance.