The total number of words that can be formed | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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:

Similar Questions

Let $n(A) = 3$ and $n(B) = 3$ (where $n(S)$ denotes the number of elements in set $S$). Then,the number of subsets of $(A \times B)$ having an odd number of elements is:

Total number of $3$ letter words that can be formed from the letters of the word $'SAHARANPUR'$ is equal to

In how many ways can the letters of the word $BALLOON$ be arranged so that two $Ls$ do not come together?

How many $4$-digit numbers are there with distinct digits?

It is required to seat $5$ men and $4$ women in a row so that the women occupy the even places. How many such arrangements are possible?

Vedclass Test Series

Exam Paper Generator

Online Exam Module