Brilliant rearrangements

Level pending

Given some permutation of the letters of the word 'BRILLIANT', the probability that no two letters which are the same (ie. both Ls or both Is) are equidistant from the central letter can be expressed as \( \frac{a}{b} \) where \( gcd(a,b)=1 \) and \( a,b \in \mathbb{N} \). Find \( a+b \).

Examples
'TLRIIABLN' would not be allowed since both Ls are equidistant from the centre.

'ITALNLBRI' would also not be allowed since both Ls are equidistant from the centre and both Is are equidistant from the centre.

'BRILLIANT' would be fine

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