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: $R, J, S, T, H, N$ ($6$ letters).Vowels are: $A, A, A$ ($3$

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: $R, J, S, T, H, N$ ($6$ letters).Vowels are: $A, A, A$ ($3$ letters).First,arrange the $6$ consonants in $6!$ ways.To ensure vowels are alternate,we place them in the gaps created by the consonants.There are $7$ possible gaps (including ends) for $6$ consonants: $\_ C \_ C \_ C \_ C \_ C \_ C \_$.We need to choose $3$ gaps out of $7$ for the $3$ vowels,which can be done in $^7C_3$ ways.Since all $3$ vowels are identical $(A)$,there is only $1$ way to arrange them in the chosen gaps.Total number of words $= 6! 	imes ^7C_3$.

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

On the occasion of the Deepawali festival,each student of a class sends greeting cards to every other student. If there are $20$ students in the class,then the total number of greeting cards exchanged by the students is:

If ${}^n P_r = {}^{(n-1)} P_r + x \cdot {}^{(n-1)} P_{(r-1)}$,$\forall n, r \in N$ and $r \leq n$,then $x =$

How many $4$-digit numbers can be formed by using the digits $1$ to $9$ if repetition of digits is not allowed?

If ${}^{2n+1}P_{n-1} : {}^{2n-1}P_n = 11 : 21$,then $n^2 + n + 15$ is equal to:

If all the words formed by using the letters of the word $CRICKET$ are arranged in a dictionary in alphabetical order,how many words appear before the word $CRICKET$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module