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Thus, the probability is $\boxed{\dfrac{25}{216}}$
Question: How many distinct words can be formed using all the letters in the word "BIOINFORMATICS" if the letters must be arranged such that all vowels appear consecutively?
Solution: First, identify the vowels and consonants in "BIOINFORMATICS".
Vowels: I, O, I, A, I → 5 vowels (I appears 3 times, O and A once)
Consonants: B, N, F, R, M, T, C, S → 8 consonants (all distinct)
Treat the block of vowels as a single "super-letter". So we are arranging:
1 vowel block
8 distinct consonants
Total entities to arrange: $ 1 + 8 = 9 $
Number of ways to arrange these 9 entities, accounting for the consonants being distinct and the vowel block unique: