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

Question

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 (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Vowels: A,A,A,I,I,O Consonants: S,S,S,S,N,N,T ∵ Total number of ways in which vowels come together =(⌊ 8/⌊ 4 ⌊ 2) × (⌊ 6/⌊3 ⌊ 2)=50400

Q. 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________

Vowels : $A, A, A, I, I, O$
Consonants : $S, S, S, S, N, N, T$
$∵$ Total number of ways in which vowels come together
$= \frac{⌊ 8}{⌊ 4 ⌊ 2} \times \frac{⌊ 6}{⌊ 3 ⌊ 2} = 50400$

Q. 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________

Vowels : A,A,A,I,I,O Consonants : S,S,S,S,N,N,T ∵ Total number of ways in which vowels come together =⌊4⌊2⌊8​×⌊3⌊2⌊6​=50400

Vowels : $A, A, A, I, I, O$
Consonants : $S, S, S, S, N, N, T$
$∵$ Total number of ways in which vowels come together
$= \frac{⌊ 8}{⌊ 4 ⌊ 2} \times \frac{⌊ 6}{⌊ 3 ⌊ 2} = 50400$