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adeimrst: 310
aeilnrst: 312
...
adeiprst: 332
aeilprst: 344
aeinprst: 346

#!/usr/bin/perl
use warnings;
...
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$ grep -E '^[aeinprst]{1,8}$' 2of12inf.txt  | grep -vE '(.).*\1' | wc 
+-l
346

$ grep -E '(.).*\1.*:' 1056884.out | tail -n1
aeiprsst: 279
$ grep -E '^[aeiprsst]{1,8}$' 2of12inf.txt | grep -Ev '([aeiprt]).*\1|
+s.*s.*s' | wc -l
279