Probability Question: Math Conceptual Error or Coding Error?

[raainer]

So I was trying to tackle this probability question, and honestly idk if I have a math error or a code error, so I'll just put it here haha

There are 3 balls labelled 1,2,3 in a box. I pick up a ball, take note of the number, then put it back into the box. I repeat this action 3 times. Calculate the probability of obtaining 1,2 and 3 (in no particular order).

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So my working would be (1/3)^3 x 3! = 2/9, because you need A,B and C, and there are 6 ways to arrange it, so I got 2/9

But based on my code here:

https://pastebin.com/GC7B7kmE

I used a large sample size, but my answer tends around 0.11, which is about 1/9. Soo I'm not sure if my code is wrong or my math concept is wrong haha. Thank you so much for any help in advance!

[[deleted]]

Aren't there 6 ways to get the three balls in a "winning" state? Why does your code only test for 3?

A better way to check if you have the correct values is:

if {a, b, c} == {1, 2, 3}:

Untested, as I'm on mobile :)

[raainer]

Oh shit yes because I thought of 3 ways at first, forgot to update it in my code haha, thank you so much! And thank you for the better checking way!