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

The number of rectangles that can be obtained by joining four of $12$ vertices of a $12$-sided regular polygon is:

In how many ways can $5$ sportsmen be selected from a group of $10$?

$5$-digit numbers are to be formed using $2, 3, 5, 7, 9$ without repeating the digits. If $p$ is the number of such numbers that exceed $20000$ and $q$ is the number of those that lie between $30000$ and $90000$,then $p : q$ is

There are $7$ men and $8$ women in a club. $A$ committee is formed using these persons. What will be the number of ways to select $6$ persons such that at least one is a woman?

In how many ways can $6$ persons stand in a queue at a time?

Vedclass Test Series

Exam Paper Generator

Online Exam Module