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

What is the total number of permutations of the letters of the word $BANANA$?

The number of three-digit even numbers,formed by the digits $0, 1, 3, 4, 6, 7$ if the repetition of digits is not allowed,is .... .

In how many ways can the letters of the word $ASSASSINATION$ be arranged so that all the $S$'s are together?

In a library,there are $a$ books of type $A$,$2$ books of type $B$,$3$ books of type $C$,and $1$ book of type $D$. In how many ways can these books be arranged?

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module