Probability of inhabited planets: I have 16 exosystems, and each system is orbited by 3 planets....

[The Highlander]

Hi Highlander. Thank you for your really good explanation. I now understand where you are coming from. The order does make a difference so, the formula would be
p = (16C11 x 3^11)/48C11 ≠≈ 4368 x 177147/2.259520036 E+10 (my calculator doesn't do combinations) ≠≈ 0.0342452
and (1 - 0.0342452) = 96.575% (to 3dp)

Yup, you've certainly got the right answer now. ?
(My only remaining quibble might be your use of "=" where you should really use "≈". ?)

My wee, Poundland 10 digit calculator (it doesn't "do" Combinations either) displays ₄₈C₁₁ as 2.25952 E10 but stores it in memory as 2.2595200368 E10 so your approximation is out on the final digit shown; it should be: 2.259520037 E+10 (if you insist on writing it down). That's why you never round anything until the final answer. (and that only gets an "equals" sign if you state your degree of accuracy (to a given number of decimal places or sig. figs.). Which, happily, you did. ?

 

[Bluebell]

Well, thanks very much everyone, and especially you Highlander! Your explanation was excellent for my visual mind. Your diagram really helped me conceptualise the problem. I don't know where you are in Scotland, (if indeed you are). My Mother is a Forbes - 'Grace me Guide' Take care, Bluebell.

 

[The Highlander]

Well, thanks very much everyone, and especially you Highlander! Your explanation was excellent for my visual mind. Your diagram really helped me conceptualise the problem. I don't know where you are in Scotland, (if indeed you are). My Mother is a Forbes - 'Grace me Guide' Take care, Bluebell.

Where else would I be? ?
Though I'm pretty much right in the middle (not really the Highlands, lol)
So you're from good stock then. ?
'Aonaibh Ri Chéile' (Let Us Unite)
(Most appropriate considering this contribution. ?)

 

[blamocur]

Well, thanks very much everyone, and especially you Highlander! Your explanation was excellent for my visual mind. Your diagram really helped me conceptualise the problem.

It is always nice -- and useful -- to get feedback, but especially the detailed one mentioning what helped the most.
Thank you!