The number of words formed from the letters o | vedclass

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

Question

(A) The word $RAJASTHAN$ contains $9$ letters: $R, A, J, A, S, T, H, A, N$.Consonants are: $R, J, S, T, H, N$ (Total $6$).Vowels are: $A, A, A$ (Total

Vedclass · Accepted Answer

$6! 	imes ^7C_3$

Vedclass · Answer

(A) The word $RAJASTHAN$ contains $9$ letters: $R, A, J, A, S, T, H, A, N$.Consonants are: $R, J, S, T, H, N$ (Total $6$).Vowels are: $A, A, A$ (Total $3$).To ensure vowels are alternate,we first arrange the $6$ consonants in $6!$ ways.These $6$ consonants create $7$ possible gaps (including ends) where the $3$ vowels can be placed: $\_ C \_ C \_ C \_ C \_ C \_ C \_$.We choose $3$ gaps out of $7$ in $^7C_3$ ways.Since all $3$ vowels are identical $(A, A, A)$,they can be arranged in the chosen gaps in only $1$ way.Therefore,the total number of words is $6! 	imes ^7C_3$.

The number of words formed from the letters of the word $RAJASTHAN$ by taking all the letters at a time in which vowels are alternate is:

Similar Questions

In how many ways can the letters of the word '$UNIVERSAL$' be arranged? In how many of these will $E, R, S$ always occur together?

The number of $6$-digit numbers that can be formed using the digits $0, 1, 2, 5, 7,$ and $9$ which are divisible by $11$ and no digit is repeated,is

$A$ group of students comprises $5$ boys and $n$ girls. If the number of ways in which a team of $3$ students can be selected from this group such that there is at least one boy and at least one girl in each team is $1750$,then $n$ is equal to:

How many $3$-digit numbers can be formed from the digits $2, 3, 5, 6, 7,$ and $9$ which are divisible by $5$,given that no digit is repeated?

In how many ways can $5$ boys and $5$ girls sit in a circle so that no two boys sit together?

Vedclass Test Series

Exam Paper Generator

Online Exam Module