In article , Terry Harper
writes
There are 13824 three-letter groups available. 3176 (23%) contain an X
or a Z. That roughly matches my perception of their frequency; have you
done a census?
This puzzled me at first, until I realised that there is a 1 in 24 chance of
getting a "Z" in each of one of the columns, which means a 1 in 8 chance of
getting a "Z" in one of the three columns.

No, that's not how you do it. In fact, there's about a 1 in 8.34 chance
of getting a "Z" in one of the three columns, because the cases with two
or three "Z"s pull the odds down.

The way to do it is like this. In each column, there are 22 ways not to
have an X or a Z. So there are 22*22*22 (10648) plates with no X or Z.
There are 24*24*24 (13824) in total, leaving 3176 with an X or Z.

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Clive D.W. Feather, writing for himself | Home:
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