The total number of words that can be formed | vedclass

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Question

(C) The word $ALLEN$ consists of $5$ letters: $A, L, L, E, N$. There are $2$ vowels $(A, E)$ and $3$ consonants $(L, L, N)$. The total number of arran

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(C) The word $ALLEN$ consists of $5$ letters: $A, L, L, E, N$. There are $2$ vowels $(A, E)$ and $3$ consonants $(L, L, N)$. The total number of arrangements of the $5$ letters is $\frac{5!}{2!}$,where $2!$ accounts for the repetition of the letter $L$. Total arrangements $= \frac{120}{2} = 60$. In these $60$ arrangements,the vowels $A$ and $E$ can appear in two orders: $(A, E)$ or $(E, A)$. Since we require the vowels to appear in alphabetical order,only one of these two arrangements is valid. Therefore,the number of favorable words $= \frac{60}{2} = 30$.

The total number of words that can be formed by using all the letters of the word $ALLEN$ such that all vowels occur in alphabetical order is:

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