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

(B) The word $MULTIPLE$ consists of $8$ letters: $M, U, L, T, I, P, L, E$. The vowels are $U, I, E$ and the consonants are $M, L, T, L$. The vowels ar

Vedclass · Accepted Answer

$360$

Vedclass · Answer

(B) The word $MULTIPLE$ consists of $8$ letters: $M, U, L, T, I, P, L, E$. The vowels are $U, I, E$ and the consonants are $M, L, T, L$. The vowels are at positions $2, 5, 8$. Keeping these positions fixed,the $3$ vowels can be arranged in $3! = 6$ ways. The remaining $5$ positions are occupied by the consonants $M, L, T, L$. The number of ways to arrange these $5$ consonants (where $L$ repeats twice) is $\frac{5!}{2!} = \frac{120}{2} = 60$. Therefore,the total number of arrangements is $3! 	imes 60 = 6 	imes 60 = 360$.

In how many ways can the letters of the word $MULTIPLE$ be arranged keeping the position of the vowels fixed?

Similar Questions

There are $6$ periods in each working day of a school. The number of ways one can arrange $5$ subjects such that each is allowed at least one period is:

The number of ways in which the letters of the word $ARRANGE$ can be arranged such that both $R$ do not come together is

Let $P$ be the set of seven-digit numbers with the sum of their digits equal to $11$. If the numbers in $P$ are formed by using the digits $1, 2,$ and $3$ only,then the number of elements in the set $P$ is:

In a train,five seats are vacant. In how many ways can three passengers sit?

The number of four-digit even numbers that can be formed using the digits $0, 1, 2,$ and $3$ without repetition is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module