How many words can be formed using the letter | vedclass

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

Question

(D) The word $INSURANCE$ consists of $9$ letters: $I, N, S, U, R, A, N, C, E$.The vowels are $I, U, A, E$ ($4$ vowels).The consonants are $N, S, R, N,

Vedclass · Accepted Answer

None of these

Vedclass · Answer

(D) The word $INSURANCE$ consists of $9$ letters: $I, N, S, U, R, A, N, C, E$.The vowels are $I, U, A, E$ ($4$ vowels).The consonants are $N, S, R, N, C$ ($5$ consonants).Since all vowels must come together,we treat the group $(I, U, A, E)$ as a single unit.Now,we have the unit $(IUAE)$ and the $5$ consonants $(N, S, R, N, C)$,making a total of $6$ units.These $6$ units can be arranged in $\frac{6!}{2!}$ ways (since $N$ repeats twice).Within the vowel unit,the $4$ vowels can be arranged in $4!$ ways.Total number of words = $\frac{6!}{2!} 	imes 4! = \frac{720}{2} 	imes 24 = 360 	imes 24 = 8640$.Since $8640$ is not among the options,the correct choice is $D$.

How many words can be formed using the letters of the word $INSURANCE$,such that all vowels always come together?

Similar Questions

The total number of words that can be formed using the letters $a, b, c, d, e, f$ taken $3$ at a time such that each word contains at least one vowel is:

How many distinct words can be formed using the letters of the word $EQUATION$ such that the word starts and ends with a consonant?

The sum of all the $4$-digit distinct numbers that can be formed with the digits $1, 2, 2,$ and $3$ is:

The number of numbers,strictly between $5000$ and $10000$,that can be formed using the digits $1, 3, 5, 7, 9$ without repetition is $..........$.

Evaluate $7! - 5!$

Vedclass Test Series

Exam Paper Generator

Online Exam Module