# For all Brilliant Members

BRILLIANT

How many words are there can be made by arranging the letters of the upper word? By Permutations with Repetition, we know there are a total of $$\dfrac{9!}{2!2!}=90720$$ words.

But that's very easy. I need something more complicated.

How many words are there can be made by arranging the letters of the word BRILLIANT such that:

• The two L's cannot stand next to each other, and

• At least 1 vowel stands between the two L's.

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