All the letters of the word 'EAMCET' | vedclass

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

Question

(C) The word '$EAMCET$' consists of $6$ letters: $E, A, M, C, E, T$.
The vowels are $E, A, E$ (where $E$ repeats twice) and the consonants ar

Vedclass · Accepted Answer

$72$

Vedclass · Answer

(C) The word '$EAMCET$' consists of $6$ letters: $E, A, M, C, E, T$.
The vowels are $E, A, E$ (where $E$ repeats twice) and the consonants are $M, C, T$.
First,we arrange the $3$ consonants $(M, C, T)$ in $3! = 6$ ways.
These $3$ consonants create $4$ gaps (represented by underscores): $ M C T $.
We need to place the $3$ vowels $(E, A, E)$ in these $4$ gaps such that no two vowels are adjacent.
The number of ways to choose $3$ gaps out of $4$ is $^4C3 = 4$.
Since there are two identical vowels $(E)$,the number of ways to arrange $E, A, E$ in the chosen $3$ gaps is $\frac{3!}{2!} = 3$.
Total arrangements = (Ways to arrange consonants) $	imes$ (Ways to choose gaps) $	imes$ (Ways to arrange vowels in gaps)
Total arrangements = $6 	imes 4 	imes 3 = 72$.

All the letters of the word '$EAMCET$' are arranged in all possible ways. The number of such arrangements in which two vowels are not adjacent to each other is

Similar Questions

If $33!$ is divisible by $2^n$,where $n \in N$,then the sum of all possible values of $n$ is:

In how many ways can a football team of $11$ players be selected from $15$ players? In how many cases can a particular player be included?

In a circus, there are $10$ cages to accommodate $10$ animals. Out of these, $4$ cages are so small that $5$ specific animals cannot enter them. In how many ways is it possible to accommodate the $10$ animals in these $10$ cages?

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?

The Chief Ministers of $11$ States of India meet to discuss the language problem. In how many ways can they seat themselves at a round table so that the Punjab and Madras Chief Ministers sit together?

Vedclass Test Series

Exam Paper Generator

Online Exam Module