The number of words,with or without meaning,t | vedclass

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(C) The word $ASSASSINATION$ contains $13$ letters: $A, S, S, A, S, S, I, N, A, T, I, O, N$.Vowels are: $A, A, A, I, I, O$ (Total $6$ vowels).Consonan

Vedclass · Accepted Answer

$50400$

Vedclass · Answer

(C) The word $ASSASSINATION$ contains $13$ letters: $A, S, S, A, S, S, I, N, A, T, I, O, N$.Vowels are: $A, A, A, I, I, O$ (Total $6$ vowels).Consonants are: $S, S, S, S, N, N, T$ (Total $7$ consonants).Treating the $6$ vowels as a single unit,we have $7$ consonants + $1$ unit = $8$ items to arrange.Number of arrangements of these $8$ items (where $S$ repeats $4$ times and $N$ repeats $2$ times) is $\frac{8!}{4!2!} = \frac{40320}{24 	imes 2} = 840$.Now,arrange the $6$ vowels within the unit (where $A$ repeats $3$ times and $I$ repeats $2$ times):Number of arrangements = $\frac{6!}{3!2!} = \frac{720}{6 	imes 2} = 60$.Total number of words = $840 	imes 60 = 50400$.

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 $.............$.

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