Find the total number of arrangements of the | vedclass

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

Question

(C) The word $EAMCET$ has $6$ letters: $E, A, M, C, E, T$.There are $2$ vowels $(E, E)$ and $4$ consonants $(A, M, C, T)$. Wait,let us re-examine the

Vedclass · Accepted Answer

$72$

Vedclass · Answer

(C) The word $EAMCET$ has $6$ letters: $E, A, M, C, E, T$.There are $2$ vowels $(E, E)$ and $4$ consonants $(A, M, C, T)$. Wait,let us re-examine the letters: $E, A, M, C, E, T$. The vowels are $E, A, E$ ($3$ vowels) and consonants are $M, C, T$ ($3$ consonants).First,arrange the $3$ consonants $M, C, T$ in $3! = 6$ ways.These consonants create $4$ gaps (including ends): $\_ M \_ C \_ T \_$.We need to place the $3$ vowels $(E, A, E)$ in these $4$ gaps such that no two vowels are together.The number of ways to choose $3$ gaps out of $4$ is $^4C_3 = 4$.Since there are $2$ identical vowels $(E, E)$,the number of ways to arrange the vowels in the chosen gaps is $\frac{3!}{2!} = 3$.Total arrangements = $3! 	imes ^4C_3 	imes \frac{3!}{2!} = 6 	imes 4 	imes 3 = 72$.

Find the total number of arrangements of the letters of the word $EAMCET$ such that no two vowels are together.

Similar Questions

The number of five-digit numbers greater than $50000$ that can be formed by using all the digits $0, 1, 3, 5, 9$ only once is

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

How many permutations can be formed from the letters of the word $ALGEBRA$ without changing the relative positions of the vowels and consonants?

In how many ways can one send $6$ new-year greeting cards to $4$ people?

How many arrangements of $3$ letters can be made from the letters $a, b, c, d, e, f$ without repetition,such that each arrangement contains at least one vowel?

Vedclass Test Series

Exam Paper Generator

Online Exam Module