In how many ways can the letters of the word | vedclass

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

Question

(C) The word $GARDEN$ has $6$ distinct letters: $G, A, R, D, E, N$.The vowels in the word are $A$ and $E$.Total number of arrangements of $6$ letters

Vedclass · Accepted Answer

$360$

Vedclass · Answer

(C) The word $GARDEN$ has $6$ distinct letters: $G, A, R, D, E, N$.The vowels in the word are $A$ and $E$.Total number of arrangements of $6$ letters is $6! = 720$.In any arrangement,the vowels $A$ and $E$ can appear in $2! = 2$ ways: $(A, E)$ or $(E, A)$.Since we require the vowels to appear in alphabetical order,we only consider the case where $A$ comes before $E$.By symmetry,exactly half of the total arrangements will have $A$ before $E$,and the other half will have $E$ before $A$.Therefore,the number of arrangements where $A$ appears before $E$ is $\frac{6!}{2!} = \frac{720}{2} = 360$.

In how many ways can the letters of the word $GARDEN$ be arranged such that the vowels appear in alphabetical order?

Similar Questions

How many words can be formed using the letters of the word $MOBILE$ such that the consonants always occupy odd positions?

The number of words which can be made out of the letters of the word $MOBILE$ when consonants always occupy odd places is

In how many ways can $6$ people be arranged in a row such that $A, B, C,$ and $D$ always appear in the order $ABCD$ (not necessarily together)?

If the letters of the word $RACHIT$ are arranged in all possible ways and these words are listed in dictionary order,what is the rank of the word $RACHIT$?

How many numbers lying between $500$ and $600$ can be formed with the help of the digits $1, 2, 3, 4, 5, 6$ when the digits are not to be repeated?

Vedclass Test Series

Exam Paper Generator

Online Exam Module