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Relevant wiki: Permutations with Repetition

Instead of counting number of words satisfy the condition, we'll count number of words don't satisfy the condition, and calculate the complement.

Note that the word BRILLIANT has $4$ consonants other than L , each is repeated once only. So, words don't satisfy the condition are words with no more than $4$ letters between the L 's.

Consider the numbers 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 . What we'll do is to replace the numbers with the letters.

If the 2 L 's stand next to each other, there will be a total of $8 \times \dfrac{7!}{2!} = 20160$ (remember there are 2 I 's, so divide by $2!$ ).

If there is exactly 1 consonant stand between the 2 L 's (in the form L - consonant - L ), there will be a total of $7 \times 4 \times \dfrac{6!}{2!} = 10080$ .

If there is exactly 2 consonants stand between the 2 L 's (in the form L - consonant x2 - L ), there will be a total of $6 \times P_2^4 \times \dfrac{5!}{2!} = 4320$ .

If there is exactly 3 consonants stand between the 2 L 's (in the form L - consonant x3 - L ), there will be a total of $5 \times P_3^4 \times \dfrac{4!}{2!} = 1440$ .

Lastly, if there is exactly 4 consonants stand between the 2 L 's (in the form L - consonant x4 - L ), there will be a total of $4 \times 4! \times \dfrac{3!}{2!} = 288$ .

Add all of them up, the number of words don't satisfy the condition is $36288$ .

Therefore, the answer is $90720 - 36288 = \boxed{54432}$ .