me think me need more than 52 man years! :(:(:(
me a biologist, not mathematician :o:o:o
Sorry, that was from P6 enrichment module.
You want to slot 30 "b"s into a string of 30 "a"s so that no two "b"s are side by side.
That means the 30 "b"s must occupy the "spaces" in between the 30 "a"s, with a maximum of one "b" in each "space". For instance, we can have something like "aababa", but not "aabbbba".
Since there are 31 spaces, including the start and end positions, there must be precisely one space left empty. Hence, the number of permutations is 31 (you just choose which space is not occupied by a "b").