The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is _____.
Step-by-Step Solution
Key Concept: Treat all vowels as a single block. Count arrangements of (consonant block + vowel block) $\times$ arrangements within vowel block.
Vowels: A,A,A,I,I,O $\to$ arrange in 6!/(3!2!) ways. Consonants+vowel block: 8 units with S,S,S,S,N,N,T $\to$ 8!/(4!2!) ways. Total = \(\frac{8!}{4!2!} \times \frac{6!}{3!2!}\) = 840 $\times$ 60 = 50400.
Correct Answer: 50400