In how many different ways can the letters of | vedclass

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

Question

(C) The word '$LEADING$' consists of $7$ distinct letters: $L, E, A, D, I, N, G$.The vowels in the word are $E, A, I$ (total $3$ vowels).To ensure the

Vedclass · Accepted Answer

$720$

Vedclass · Answer

(C) The word '$LEADING$' consists of $7$ distinct letters: $L, E, A, D, I, N, G$.The vowels in the word are $E, A, I$ (total $3$ vowels).To ensure the vowels always come together,we treat the group $(E, A, I)$ as a single unit or entity.Now,we have the letters ${L, D, N, G}$ and the single unit $(E, A, I)$.This gives us a total of $4 + 1 = 5$ entities to arrange.These $5$ entities can be arranged in $5!$ ways.$5! = 5 	imes 4 	imes 3 	imes 2 	imes 1 = 120$.Within the group $(E, A, I)$,the $3$ vowels can be arranged among themselves in $3!$ ways.$3! = 3 	imes 2 	imes 1 = 6$.Therefore,the total number of arrangements is $5! 	imes 3! = 120 	imes 6 = 720$.

In how many different ways can the letters of the word '$LEADING$' be arranged in such a way that the vowels always come together?

Similar Questions

There are $6$ candidates for $3$ posts. In how many ways can the posts be filled?

The number of triangles that can be formed by choosing the vertices from a set of $12$ points,$7$ of which lie on the same straight line,is

The number of ways in which an examiner can assign $30$ marks to $8$ questions,awarding not less than $2$ marks to any question is

The number of ways in which $5$ boys and $3$ girls can be seated on a round table if a particular boy $B_1$ and a particular girl $G_1$ never sit adjacent to each other,is

The total number of $4$-digit numbers which can be formed using the digits $1, 2, 3, 4$ without repetition such that the digit $n+1$ never immediately follows the digit $n$ (for $n=1, 2, 3$) is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module